My argument for using the words the specific game uses is so that DMs and players don't conflate the mechanics and processes of one game and a different game and thereby risk the game not working as intended, potentially leading to an undesirable play experience. I like to keep a nice strong firewall between how different games handle things unless I
purposefully make changes to have one game be more like the other. I learned to do this years ago when I realized my D&D 4e game wasn't going as well as my D&D 3.Xe games were going, and that was because I was running the game as if it was a different game. A lot of DMs do this in my experience to the detriments of their campaigns.
"Skill checks" exist in D&D 4e, for example. In D&D 4e, the game comes right out and says players often initiate a skill check by asking the DM if he or she can make one.
Almost always, the D&D 4e rules say, the DM says "Yes." Contrast that with D&D 5e which says nothing of the sort when it comes to ability checks, except that the player may ask if a particular skill proficiency applies to the ability check.
If I come from a background of running and playing D&D 4e (as I do), I might be tempted to think of ability checks in D&D 5e the same way as skill checks in D&D 4e - players ask to make checks and the DM says "Yes." As a result, I'm going to end up with a different game experience than what may be intended.
Will my game be terrible if that happens? No, probably not. But it definitely won't look like a D&D 5e game where players describe what they want to do without asking to make ability checks. Or what I would consider the smart play of
trying to avoid ability checks as often as possible. You won't
ever catch a regular player in my game asking to make a check. It's just not the smart play to
want to roll a fickle d20. Working to remove uncertainty as to the outcome and/or the meaningful consequence of failure is the way to go. Sometimes you can't, but you damn sure try. And that game is going to look different than a game where players ask to make checks.
So, when I'm engaged in a discussion on the forums about these things, I make the effort to be reasonably specific and consistent in the language I use, especially if I'm referencing game terms that have a specific meaning in the given game's rules. It's not about being pedantic, but rather being accurate and trying to make sure I'm not conflating one game with another game or leading others to do the same.
@DM Dave1 and
@Elfcrusher had it absolutely right when they asked upthread which game the OP was referring to. Without a tag to identify this as a D&D 5e thread, we could well have been talking about D&D 3.Xe or D&D 4e, and how those games handle these issues can be different.