I could use a better name for this (any suggestions?), but I'll use "distinctions of the moment" for the moment.
A distinction of the moment is a distinction made between two synonyms or near-synonyms (or sometimes antonyms), for the sake of pointing out a difference which is important to the discussion at hand. For example, I might contrast "knowledge" and "understanding" for the sake of a discussion about memorization-and-regurgitation style education vs focusing more on reasons. In a different conversation, I may well use "knowledge" vs "understanding" to talk about knowing-how vs knowing-what (and I might well call either of those two "understanding" and the other "knowledge" -- it doesn't matter, it's just a distinction of the moment).
The important thing about distinctions of the moment is that they just have to be made clear for the purpose of the conversation, and can be thrown away afterwards. This fails if someone thinks that they need to argue the definition of a word as if it were a sacred duty. Perhaps I make a distinction between "liberal" and "progressive" for the purpose of conversation, and someone takes issue with it because they've got a favorite definition of one or both of those terms which they think is importantly correct. This is not useful to the conversation.
A pet peeve of mine is that a lot of people seem to carry around distinctions-of-the-moment forever, as if they were true subtle differences in the meanings of words. I feel this way about distinguishing between "sympathy" and "empathy" -- I'm not sure quite why, but it seems to me that the distinction people tend to draw between the two is something which is just not generally useful enough to be more than a distinction-of-the-moment. The two words have different usage patterns, yes, but I don't think those usage patterns are really well-explained by "feeling emotion in response to others vs putting yourself in their shoes".
Yeah, I don't think I've successfully drawn a line around the cases which annoy me. Here are some of the things that come to mind:
The words really are near-synonyms.
The definition offered doesn't fit the usage, even of the person offering the definition. I think the sympathy/empathy example illustrates this; lots of people will give a verbal explanation of the difference between the two, but it seems only shallowly based on usage differences, if at all.
The definitions offered are claimed to be general, rather than special case (which, especially in combination with the previous point, makes me tend to think that the person doesn't know how words work -- or at least, makes me think they aren't a person who is aware of how words can fluidly adapt to the needs of the conversation).
The distinction being offered isn't particularly crafted to fit the situation. (I may develop a suspicion that the person is mentioning the distinction just to sound smart -- something which might not annoy me in other contexts, but does annoy me when I identify it as a mis-used distinction-of-the-moment.)
The distinction offered doesn't strike me as particularly generally useful. I'll forgive all the previous points if someone is giving a distinction which I find illuminating.
Sometimes you want to talk about "A1 vs A2" and sometimes you want to talk about "A vs Z".
Maybe the distinction between A1 and A2 is rarely made, and most people just perceive them both as a general A, but today you want to talk exactly about those differences, so you need to make the difference clear by putting unusually large emphasis on the differing details. (Maybe the language doesn't even have three different words for A, A1, A2; sometimes there is just one word for both A and A1, and people would say e.g. "A in the wider/narrower sense of the word".)
But the next day you want to talk about differences between A and Z in general, and anyone who focuses on differences between A1 and A2 is losing the larger picture... well, unless those differences between A1 and A2 are actually relevant for the "A vs Z" debate you are trying to have; but in such case, the person insisting on the difference should explain how specifically it is relevant.
Essentially, greater precision comes with greater costs, so the person who increases the cost should communicate the cost-benefit analysis to their partners in the debate. Sometimes the extra cost benefits everyone by helping them reach better conclusions. Sometimes the extra cost only benefits the speaker by allowing them signal greater sophistication. Sometimes the speaker is not even aware that these two cases are different (i.e. they may be merely signalling, but it's not an intentional defection, only just blindly copying what they saw other people do in similar situations). Sometimes the speaker is too mindkilled about "A1 vs A2", e.g. because it has huge political connotations for them, so they are emotionally opposed to using "A" as an umbrella term for both.