Difference between Bughouse and Crazyhouse

Per title. 

Is there any particular differences beside the time management?

Bughouse is a game for 4 players, using 2 Chess boards. Crazyhouse is a game for 2 players, using one Chess board.

Otherwise they are the same. Not sure how the time management comes in.

Crazyhouse is a two player bughouse. When you capture a piece then you recieve the piece in your own color. On subsequent turns, you may make a traditional chess move or drop the new piece on an unoccuppied square (pawns can not be dropped on first or last rank). There is an advantage to playing white in zh (crazyhouse) and the tactical fury is quite entertaining. I need a knight, so i take him and then relay him next turn in order to get the fork. The openings are more chess normal because you do not have to concern yourself for your partner's oversight. Nothing can happen on the board that you can not see unlike a partner blundering something away leaving you in a poor position. The time management matters like normal chess. You spend to much time now then pay for it later. Unlike bughouse where a few seconds are worth a piece at the highest levels.

I daresay that Bughouse is more complex for computers simply because of the time management and how tricky it can be. 

Board #1 have winning position.

Board #2 stopped moving since the parner will win. 

Now board 2 have to calculate how long he can remain passive until he have to move to avoid forfeit on time. 

Crazyhouse is the 2-player chess version of Bughouse.

Another difference is in Crazyhouse, the pieces you captured are reversed to your side. Whereas in Bughouse, the pieces you captured stay the same color.

You can drop a piece anywhere on the board but it has to be an empty square. Pawns may not be dropped on the 1st and 8th rank.