To be clear, I wasn't arguing that the terms -should be- interchangeable, I was observing that people often use them interchangeably and typically everyone involved in the conversation understands what's meant.
I still think you're arguing for the existence of rules that were never actually established. Precedents perhaps, but not rules.
I don't know about precedent v. rules. One thing that all the time travel had in common--the timeline was in danger.
Honestly, I don't see that. For starters, the only canon evidence we have is what is on screen, by your own admission. Books and comics don't count. So, we have to accept that Spock's behavior is in fact in character for the situation. Since Spock has seen time travel before, as well as alternate universes, then he would be familiar with the mechanics of it. No, it's not one the nose but Spock's behavior is sufficient explanation for me. Similarly with Kelvin Spock's own response to Uhura's "an alternate timeline."
An alternate timeline actually brings up my point--that conversation on the bridge does not make the case that the prime timeline exists. Any alternate timeline/reality would happen whether the prime universe exists or not. That might be the biggest problem--that conversation didn't explain a thing. If I go to another universe, I'm in an alternate realty/timeline, especially if I'm in the past, and I find things are different. If I travel in time and erase the timeline, I am also in an alternate reality/timeline. Nothing indicates whether my original timeline exists. As for Spock, unfortunately, they don't go into his behavior in the movie at all. Maybe he feels he is too old to fix the problem alone.
How many different types of time travel have we seen in Star Trek? In TOS I think I can recall at least 3 possibly 4. We also have the Defiant traveling both back in time as well as jumping universes. Then there's the whole timeship thing which is able to reintegrate people from multiple timelines back in to one person. You have multiple quantum realities occurring in Parallels with nigh infinite branches from singular events. At some point in time any "rules" are going to become guidelines without much of an eye bat.
No argument that there aren't plenty of different time travel methods. But quantum realities and time travel are different animals. I have no doubt that even if the prime universe is erased, another universe exactly like it exists where Spock and Nero didn't time travel. But the way it went down in ST09, they did not do the prime universe any favors. All the more reason to do a sequel.
And I would love to see something. I heard the unused Orci script was going to do that instead of Beyond. But I'll never know since no one has seen it.