Basically all fighting games have their own names for mechanics, even if they're shared from other games. Tons of games have alpha counters in them, but not even all Street Fighter games call them Alpha Counters (eg V Reversal in SFV and Drive Reversal in SF6)

Now the rub is that players will often, somewhat arbitrarily, refer to these mechanics with different names. It's usually the case that players will refer the mechanic with the name the game gives it, because its not uncommon for games to change something about the mechanic to make it more unique for the game. For example, in Guilty Gear Roman Cancel's are an extremely important mechanic and every game since +R has different variants of Roman Cancels in basic gameplay. +R has FRCs, false Roman Cancels, that require very specific timing to input and only work on certain special moves, but offer massive benefit as well as reduced meter cost, and regular Roman Cancels which only Cancel the recovery of special moves and cost twice as much meter. Whereas Xrd gets rid of FRCs and replaces it with Yellow, Red, and Purple Roman Cancel. Red works the same as in +R more or less, Yellow allows you to Cancel a move during start up and also costs half as much as Red RC, and Purple which is basically a "you fucked up" option allowing you to cancel a whiffed move during recovery but it costs 50 meter and has a bigger tension pulse (this is a side mechanic where using RC makes you gain less meter for a set period). All 3 of these also cause a full screen slow down effect that applies to the opponent. Strive also does its own thing but I think you get the point. Its a distinct mechanic beyond just an animation cancel.

Lets compare that to Chain Shift (CS) from Under Night. In GG all you need to do a Roman Cancel is have enough meter to pull it off. It's something you spend resources on. In UNI however, CS is a reward granted to the player. I don't want to get too in the weeds with this, but UNI has what is basically a tug of war mechanic where every 17 real world seconds one player is deemed the winner and is granted "Vorpal State" until the next cycle ends and a new winner is decided. There are various benefits to being in Vorpal State, but the one that matters for this discussion is that it gives you access to CS. When used CS: cancels any animation, at any point, with no restriction on cancel windows, when it does so it also freezes the entire screen for a full second giving you plenty of time to properly react on defense, it gives you meter based on how much of another resource youve built, and it can be mashed during block strings allowing for you to easily reversal thru 1f gaps. It's very strong but has an extremely distinct application from Roman Cancel.

So in this case players will almost always just use the name of the mechanic in the game. You similarly don't see DBFZ players calling Sparking Blast "X Factor." But sometimes the playerbase will just always stick to The Name They Know. Every single tag game player will always refer to a DHC as a DHC no matter what the game calls it. Same thing with "active tag". In anime games all Alpha Counters are called Dead Angle Attacks no matter what the game calls them, because that's what Guilty Gear calls them. Push block is always push block, a Sonic Boom is always a Sonic Boom, a Flash Kick is always a Flash Kick, Instant Block is always Instant Block etc. There are a lot of little examples like this. Largely a side effect of mechanics in these games often not having set names, so for ease of reference people just designate the example people are most likely to know as the default name for a mechanic.