Well, there are two issues going on. One is what did they intend before TNG came around? Well honestly, probably not a whole lot. It was established pretty clearly I thought that the Eugenics Wars takes place in 1992 to 1996, that was in the dialogue. And in "Space Seed" I think the intent was that it was a 'World War', though they never said 3rd World War or World War III. I imagine the writers were intending it on being WWIII, but as it really wasn't important to the story they wanted to tell they probably just didn't give it much thought beyond what it added to the story.
I do think in "Bread and Circuses" we can say there were at least 3 World Wars. Now I happen to believe that there were only 3 World Wars because why would Spock stop there? I mean he could say the 321 million who died in your 4 World Wars (I made that number up just for the sake of argument). Now the dialogue maybe is a bit clumsy, with him saying your first 3 World Wars. It could also be that he was inferring things on Earth weren't as settled as they were later stated to be in later shows (I mean, honestly we don't know a whole lot about Earth from the original series) and maybe he thought there was a possibility of a 4th occurring in the future.
The 2nd issue is what is known now. Nowadays I believe they were separate conflicts. The Eugenics Wars, then WWIII which we have some more specific information. And the fact that novels have written them as separate conflicts lends credence to that idea. Like I said, they can't conflict with canon so if it was otherwise they wouldn't be allowed to write them as such. Now that doesn't stop a future show from rewriting Star Trek history---shows can do that----but books cannot. So at this point, since they are noted to be separate conflicts in Trek history---the Eugenics Wars in the 1990s and WWIII in the mid 21st century, that's how I take them now.
As far as Cox's novels go, even he noted I believe in his acknowledgements (or maybe later comments) that it wasn't perfect. He took up the challenge of trying to reconcile "Trek" history with real world history. But it was never going to be perfect since the 1990s had already occurred and there were really no Eugenics Wars. It's more of a how it could have happened, and that's the spirit I took it in. I always enjoy books that try to reconcile plot holes in canon. How do we make a square peg fit in a round hole. It's not the only thing I enjoy about books, but it is one of the things.
Let us remember what is actually said.
The Eugenics Wars did not happen from 1992 to 1996. The only statement about the era of the Eugenics Wars is:
SPOCK: Hull surface is pitted with meteor scars. However, scanners make out a name. SS Botany Bay.
KIRK: Then you can check the registry.
SPOCK: No such vessel listed. Records of that period are fragmentary, however. The mid=1990s was the era of your last so-called World War.
MCCOY: The Eugenics Wars.
SPOCK: Of course. Your attempt to improve the race through selective breeding.
This indicates that probably the entire "last world war"/Eugenics Wars happened during a longer or shorter part of the mid-1990s. The mid 1990s would be roughly the period from 1993.333 to 1966.666 - in the calendar used in "Space Seed".
So the Eugenics Wars should have lasted for minutes, or hours, or days, or weeks, or months, or years, and were probably entirely within the period of 1993.333 to 1996.666 SS ("Space Seed" calendar). But it is possible that the earliest parts of the Eugenics Wars were before 1993.333 SS and/or the latest parts of the Eugenics Wars were after 1996.666 SS.
What did happen from 1992 to 1996 was the reign of Khan "Midnightian" Singh, as I like to call him.
KIRK: Name, Khan, as we know him today. (Spock changes the picture) Name, Khan Noonien Singh.
SPOCK: From 1992 through 1996, absolute ruler of more than a quarter of your world. From Asia through the Middle East.
More than a quarter of Earth should mean either more than a quarter of Earth's entire surface, land and sea, or else over a quarter of the entire surface area of Earth, or over a quarter of the total human population of Earth. It is not specified how Khan acquired rule over more than one of the nations that existed in our timeline when the script was written. It isn't stated whether Khan gained power in one huge country or many small countries in the Star Trek universe, whether violently or peacefully, legally or illegally.
KIRK: Common courtesy, Mister Spock. He'll spend the rest of his days in our time. It's only decent to help him catch up. Would you estimate him to be a product of selective breeding?
SPOCK: There is that possibility, Captain. His age would be correct. In 1993, a group of these young supermen did seize power simultaneously in over forty nations.
KIRK: Well, they were hardly supermen. They were aggressive, arrogant. They began to battle among themselves.
SPOCK: Because the scientists overlooked one fact. Superior ability breeds superior ambition.
KIRK: Interesting, if true. They created a group of Alexanders, Napoleons.
So over forty countries were seized by young supermen in coups in 1993. More than a quarter of the Earth (Khan's realm) plus more than forty nations should add up to a large proportion of the total Earth ruled by those supermen.
And apparently they eventually began to attack each other.
KIRK: Well, they were hardly supermen. They were aggressive, arrogant. They began to battle among themselves.
After Khan was identified:
MCCOY: The last of the tyrants to be overthrown.
SCOTT: I must confess, gentlemen. I've always held a sneaking admiration for this one.
KIRK: He was the best of the tyrants and the most dangerous. They were supermen, in a sense. Stronger, braver, certainly more ambitious, more daring.
SPOCK: Gentlemen, this romanticism about a ruthless dictator is
KIRK: Mister Spock, we humans have a streak of barbarism in us. Appalling, but there, nevertheless.
SCOTT: There were no massacres under his rule.
SPOCK: And as little freedom.
MCCOY: No wars until he was attacked.
So apparently Khan didn't attack any other countries during his rule, and so became, by unspecified methods, the ruler of a vast preexisting country or empire in 1992 instead of conquering a bunch of countries over several years until 1992. Khan was attacked by other powers, maybe countries ruled by other supermen, or countries not ruled by supermen, or by rebels, or by a combination, and was the last of the tyrants to be overthrown.
At the dinner:
KHAN: Adventure, Captain. Adventure. There was little else left on Earth.
SPOCK: There was the war to end tyranny. Many considered that a noble effort.
So apparently there was a struggle against the supermen dictators as well as struggles among them.
SPOCK: Because the scientists overlooked one fact. Superior ability breeds superior ambition.
KIRK: Interesting, if true. They created a group of Alexanders, Napoleons.
SPOCK: I have collected some names and made some counts. By my estimate, there were some eighty or ninety of these young supermen unaccounted for when they were finally defeated.
KIRK: That fact isn't in the history texts.
SPOCK: Would you reveal to war-weary populations that some eighty Napoleons might still be alive?
So the superior ambition of the supermen is the reason why some of them attacked Khan. And note that when the wars were over the surviving normal humans apparently believed that all of the augments were dead. Every super man, super woman, and super child among them. This indicates that the war to end tyranny was also a war to exterminate all tyrants and potential tyrants.
In TNG "A Matter of Time" Picard said:
PICARD: Yes, Professor, I know. What if one of those lives I save down there is a child who grows up to be the next Adolf Hitler or Khan Singh? Every first year philosophy student have been asked that question ever since the earliest wormholes were discovered. But this is not a class in temporal logic. It's not theoretical, it's not hypothetical, it's real. Surely you see that?
So Picard compares Khan to Hitler. I doubt if Kirk & would have remembered good things about Khan if they thought Khan was as evil as Hitler. So apparently the opinions about Khan have changed in about 90 years between TOS and TNG, and something which Khan did is now considered in the era of TNG to be much more evil than Kirk & Co. considered it to be in the era of TOS.
SPOCK: Your Earth was on the verge of a dark ages. Whole populations were being bombed out of existence. A group of criminals could have been dealt with far more efficiently than wasting one of their most advanced spaceships.
This sounds like ICBMs with nuclear warheads were used and that entire countries were devastated. Possibly entire tiny countries like Antiqua and Barbuda, or Andorra, or Singapore, or maybe entire vast countries like the USA, Brazil, Russia, China, India, etc. Total casualties could have been millions, tens of millions, hundreds of millions, or billions.
And I can imagine that possibly Khan detected missiles heading toward his realm - Khantopia, or Khanistan, or whatever it was called - and pushed the button to retaliate with missiles of his own. And perhaps Picard, unlike Kirk & Co., can't forgive Khan for doing so.
There is evidence about which wars were on the list of Earth's world wars which Spock studied (possibly in some Why Humans are Inferior class on Vulcan):
In "City on the Edge of Forever":
SPOCK: This is how history went after McCoy changed it. Here, in the late 1930s. A growing pacifist movement whose influence delayed the United States' entry into the Second World War. While peace negotiations dragged on, Germany had time to complete its heavy-water experiments.
KIRK: Germany. Fascism. Hitler. They won the Second World War.
So the Second World War in Kirk's history books is similar to the one in our history. But possibly different:
SPOCK: This is how history went after McCoy changed it. Here, in the late 1930s. A growing pacifist movement whose influence delayed the United States' entry into the Second World War. While peace negotiations dragged on, Germany had time to complete its heavy-water experiments.
KIRK: Germany. Fascism. Hitler. They won the Second World War.
SPOCK: Because all this lets them develop the A-bomb first. There's no mistake, Captain. Let me run it again. Edith Keeler. Founder of the peace movement.
KIRK: But she was right. Peace was the way.
SPOCK: She was right, but at the wrong time. With the A-bomb, and with their V2 rockets to carry them, Germany captured the world.
KIRK: No.
SPOCK: And all this because McCoy came back and somehow kept her from dying in a street accident as she was meant to. We must stop him, Jim.
This suggests to me that in the alternate universe of Star Trek some evil time traveler or alien went to Germany in the early 1930s and convinced the Nazi leadership before they even came to rule Germany (and possibly separately convinced the leaders of the German armed forces) that atomic weapons carried by shorter range missiles and even ICBMS were necessary for Germany to win the next war, probably using a lot of future evidence and/or alien technology to convince them. Or maybe using some sort of mind control.
So the Germans atomic bomb and missile programs would then work together to build atomic bombs that would fit on their rockets, and rockets powerful enough to carry the bombs to distant continents, unlike as in our alternate universe. And the time traveling or alien person or persons who interfered with Earth history in the alternate universe of Star Trek must have changed the way the Nazis did things.
In Patterns of Force":
SPOCK: Quite correct. For the last few years, the real power has been Melakon.
KIRK: Gill. Gill, why did you abandon your mission? Why did you interfere with this culture?
GILL: Planet fragmented. Divided. Took lesson from Earth history.
KIRK: But why Nazi Germany? You studied history. You knew what the Nazis were.
GILL: Most efficient state Earth ever knew.
SPOCK: Quite true, Captain. That tiny country, beaten, bankrupt, defeated, rose in a few years to stand only one step away from global domination.
KIRK: But it was brutal, perverted, had to be destroyed at a terrible cost. Why that example?
SPOCK: Perhaps Gill felt that such a state, run benignly, could accomplish its efficiency without sadism.
KIRK: Why, Gill? Why?
GILL: Worked. At first it worked. Then Melakon began take over. Used the. Gave me the drug.
So in the alternate universe of Star Trek Nazi Germany is known by historians to have been a highly efficient state, unlike in our alternate universe where Nazi Germany is known by historians to have been very inefficient, which helped prevent a Nazi victory in Would war II in our timeline.
In "Bread and Circuses" a partial list of world wars from Earth history is given:
SPOCK: I said I understood it, Doctor. I find the checks and balances of this civilisation quite illuminating.
MCCOY: Next he'll be telling us he prefers it over Earth history.
SPOCK: They do seem to have escaped the carnage of your first three world wars, Doctor.
MCCOY: They have slavery, gladiatorial games, despotism.
SPOCK: Situations quite familiar to the six million who died in your first world war, the eleven million who died in your second, the thirty seven million who died in your third. Shall I go on?
The First World War in this list should be roughly equivalent to our World War I, the Second World War in this list should be roughly equivalent to our World War II (it was identified with it by Kirk in "City on the Edge of Forever"), and the Third World War in this list would be sometime after World War II and it is entirely unspecified who fought against who where and why.
Note that Spock says that only "six" million died in their version of World War I, "only" eleven million died in their version of World War II, and "only" thirty seven million died in their version of World War III.
Note that about nine to eleven million military personnel died in our World War I with about eight million civilians, thus making our deaths about 1.5, 1.8333, 2.8333, or 3.1666 times as many as in the alternate universe of Star Trek. So I deduce the World War I in the alternate universe of Star Trek was much smaller than in our universe.
https://en.wikipedia.org/wiki/World_War_I_casualties
Note that about fifty to fifty six million people, military and civilian, were killed in our World War II with about nineteen to twenty eight million more deaths from war-related famine and disease for a total of about sixty nine to eighty four million, or else fifty to fifty five million civilian deaths plus twenty one to twenty five million military deaths for a total of about seventy one to eighty million deaths. These figures make our deaths about 6.2727, 6.4545, 7.2727, or 7.6363 times as many as the "mere" eleven million in the alternate universe of Star Trek. So I deduce the World War II in the alternate universe of Star Trek was much smaller than in our universe.
And it seems to me that in the 1960s when "Bread and Circuses" was written, people feared that World War III might cause many times as many as the "mere" thirty seven million deaths in the World War III in the alternate universe of Star Trek, and possibly happened earlier than the late 1960s, possibly so early that there were far fewer weapons of mass destruction available and far fewer deaths than would have happened in the 1960s.
Was the World War III of "Bread and Circuses" Earth's last world war? Spock did mention "your first three world wars", strongly implying there has been at least one more by their time. And in "Space Seed":
SPOCK: No such vessel listed. Records of that period are fragmentary, however. The mid=1990s was the era of your last so-called World War.
MCCOY: The Eugenics Wars.
SPOCK: Of course. Your attempt to improve the race through selective breeding.
One possibility is:
1) Star Trek's First World War happens close to the time of our First World War, but is much smaller.
2) Star Trek's Second World War happens close to the time of our Second World War, but is much smaller.
3) Star Trek's Third World War happens some time after the Second World War, and is also known as the Eugenics Wars. Whole populations are bombed out of existence, but those are the populations of relatively small countries, so the total fatalities are "only" thirty seven million. This happens in the 1990s of the "Space Seed" calendar, and is Earth's last world war.
Another possibility is:
1) Star Trek's First World War happens close to the time of our First World War, but is much smaller.
2) Star Trek's Second World War happens close to the time of our Second World War, but is much smaller.
3) Star Trek's Third World War happens some time after the Second World War, - the who, what, when, where, why, and how are almost totally unknown. The total fatalities are thirty seven million.
4) Star Trek's Fourth World War happens some time after the Third World War, and is also known as the Eugenics Wars. Whole populations are bombed out of existence, so the total fatalities may be millions, tens of millions, hundreds of millions, or even billions. This happens in the 1990s of the "Space Seed" calendar, and is Earth's last world war.
Another possibility is:
1) Star Trek's First World War happens close to the time of our First World War, but is much smaller.
2) Star Trek's Second World War happens close to the time of our Second World War, but is much smaller.
3) Star Trek's Third World War happens some time after the Second World War, - the who, what, when, where, why, and how are almost totally unknown. The total fatalities are thirty seven million.
4) One or more other world wars happen after Star Trek's Third World War and before Star Trek's "Latest" World War. Nothing is known about them.
5?) Star Trek's "Latest" World War, numbered as the Fifth World War or higher, happens some time after the earlier World Wars, and is also known as the Eugenics Wars. Whole populations are bombed out of existence, so the total fatalities may be millions, tens of millions, hundreds of millions, or even billions. This happens in the 1990s of the "Space Seed" calendar, and is Earth's "latest" world war.
These are possibilities suggested by data in in TOS.
Continued:in post number 42:
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