Crack, patch nd keygen: Difference between crack, patch and key-gen

The difference between a crack and a key-gen is that

The key-gen generates a key to unlock the sotware.

A crack may consist of a patch which modifies the software so you are not requested to register anymore.
A crack is file that you need to copy into the program directory, replacing a file, to make the program work without a cd or whatever.

Patches just fixes glitches in the program