What does Kirk say in "Tomorrow is Yesterday"?
CHRISTOPHER: Must have taken quite a lot to build a ship like this.
KIRK: There are only twelve like it in the fleet.
CHRISTOPHER: I see. Did the Navy
KIRK: We're a combined service, Captain. Our authority is the United Earth Space Probe Agency.
Note that Kirk doesn't say there are only 12 other ships not including the the
Enterprise like it in the fleet, nor does he say that there are only 12 like it including the
Enterprise.
Thus Kirk doesn't say clearly whether there are 12 or 13 such ships including the
Enterprise itself.
KIrk also doesn't say there are only 12 ships of the same class as the
Enterprise. He just says "Like it".
Kirk doesn't say there are 12 "Very, very, very similar to it" or 12 "vaguely similar to it". He just says "like it" leaving it unspecified how much like it a ship has to be to count as "like it" in Kirk's eyes.
Possibly the Federation has hundreds of space warships as powerful as the
Enterprise in their defense fleets, and hundreds of science vessels with labs like the the
Enterprise has, but only a dozen ships which, like the
Enterprise, are equipped with weapons as powerful as any war ship and science labs as numerous and well starffed as any science vessel.
What does Commodore Stone say in "Court Martial"?
STONE: Stop recording. Now, look, Jim. Not one man in a million could do what you and I have done. Command a starship. A hundred decisions a day, hundreds of lives staked on you making every one of them right. You're played out, Jim. Exhausted.
In Earth history, many nations have had less than one million times as many people as they had top of the line war ships.with captains. In real life a lot more than one man in a million can command a major warship.
So presumably Stone's starships are not Starfeet defense ships, no matter how powerful the defense ships might be. Stone says:
A hundred decisions a day, hundreds of lives staked on you making every one of them right.
Real ife commanders of major warships don't have to make a hundred life or death decisions every day.,not in times of peace. And even during war they might not have to make more than one or two life ordeath decisions every day.
But an exploring ship out on the unknown fronteris could face dangers of various types much more often than a war ship in the defense fleet that usually stays in a central location in the space realm until needed.
So Stone seems to restrict starships to exploring ships.
In "The Deadly Years" Commodore Stocker wants to reach Starbase 10 with its labs to find a cure for the aging of KIrk & co., but Kirk says the
Enterprise has labs, and they end up finding a cure, and Stocker admits there is nothing a starbase can do that a starship can't do - with the right commander.
In "Bread and Circuses":
CLAUDIUS: Admit it. You find these games frightening, revolting.
KIRK: Proconsul, in some parts of the galaxy I have seen forms of entertainment that makes this look like a folk dance.
CLAUDIUS: Certain this isn't different, Captain? Those are your men dying, not strangers.
KIRK: I've had to select men to die before so that others could be saved.
CLAUDIUS: You're a clever liar, Captain Kirk. Merikus was a spaceship captain. I've observed him thoroughly. Your species has no such strength.
MERIK: He commands not just a spaceship, Proconsul, but a starship. A very special vessel and crew. I tried for such a command.
Clearly Merik considers starships to be very special, perhaps much more so than the typicat Starfleet vessel.
In "The Doomsday Machine":
PALMER: Sir, I'm picking up a ship's disaster beacon.
KIRK: Try to raise it, Lieutenant.
SPOCK: I have it on the sensors, Captain. By configuration, a starship stopped in space. She appears to be drifting.
So Spock says that the ship detected by the sensors has the configuration of a starship. Thus it seems logical that all starships have the same configureation, and that other shis p do not have that configuration.
So it is possible that all starships have a saucer shaped primary hull, a rougly cylindrical engineering hull, and two cylinddrial nacelles, with three struts joining the parts together. And it is posible that there are several different classes of starships with variations on that basic design.
And I point out that using models and clips of the
Enterprise to represent other starships might be a cost saving mesaure and that those starships might not have actually looked as much like the
Enterprise as they were shown to look.
The NCC-1701 is described as a starshp class vessel in its dedication plaque on the bridge. And a coupld of diagrams mention the
Constitution class. But I don't know if anyone can read those images well enough to see the names of the ship classes.