Well on lichess there are 5 different categories (ultrabullet, bullet, blitz, rapid and classical), but chess.com generalises to only 3 categories (bullet, blitz and rapid).
Either way though, 1|0 and 2|1 are going in the same category (bullet). Otherwise, you might as well have a new rating category for every different time control, which would get ridiculous.
Hello everyone,
I was playing live 1|0 chess today against the computer and found that I was easily crushed by a 1600 rated computer, while I would beat a real 1600 player at least 9 times out of 10 in a 1-minute chess match. This is undoubtedly because the computer's rating was inflated by 2|1 games against other players; the computer moves extremely fast (I think a tenth of a second for most moves) in both time controls despite the fact that there is increment in 2|1, so the human player can actually capitalize on the computer's mistakes in this time control. However, in "real" bullet, 1|0 chess, it is much harder to play against this playstyle.
Now, normally, I would simply suggest that the computer take slightly more time to move, or that there were different computers for each time control rather than each category (blitz, bullet, etc.). However, I realized that even for humans, 1|0 and 2|1 chess are quite distinct. In my opinion at least, a rating of 2200 from playing games with 1 minute time control is much more impressive than a rating of 2200 from playing games with a 2|1 time control (probably because most stronger players only play online chess for the faster time controls-- 1|0 is probably a lot less fun OTB). So I think this warrants a distinction between the rating acquired from playing these two time controls. What do you think, my fellow chess players?