difference between blitz, bullet, and rapid game modes


The length of the time control.
Bullet is generally 1-3 minutes.
Blitz is anything over 3 and less than 10 minutes.
Rapid is anything 10 minutes and over.

The official rulings are:
A.1
A ‘Rapid chess’ game is one where either all the moves must be completed in a fixed time of more than 10 minutes but less than 60 minutes for each player; or the time allotted plus 60 times any increment is of more than 10 minutes but less than 60 minutes for each player.
B.1
A ‘blitz’ game is one where all the moves must be completed in a fixed time of 10 minutes or less for each player; or the allotted time plus 60 times any increment is 10 minutes or less.
https://handbook.fide.com/chapter/E012018