what are the differences between these chess variations?

Checkmate haha

The difference between bullet, blitz, rapid, and classical is that the amount of time given to play the game is different. (classical > rapid > blitz > bullet) They are treated as different games, because the amount of time players can spend is different. As it goes to bullet, players become more dependent on intuition, and as it goes to classical, calculation becomes more important. So some players who are good at bullet can be weak at classical, and some players who are good at classical can be weak at bullet.
 Chess 960 is one of the variations of chess where all pieces are placed randomly(following some rules).

I see, thanks so much for the explanation

Bullet, blitz, rapid and classical chess represent the time control used in a game. In other words, the duration of the game decides which category it belongs to. The definition varies over the board and across sites, but typically a rapid time control over the board lasts for more than 15 minutes per player (for example, a time control of 25 minutes per side, with no increment, counts as a rapid game).

Chess 960, bughouse, crazyhouse, 3-check, king of the hill, atomic chess etc are variants of the game, each with varying rules from the usual standard rules, or with extra rules added to the usual standard rules. For example, in crazyhouse, capturing an opponent's piece results in you being able to "summon" the captured piece onto your board on a chosen square on your turn.