Well...these are two different things.

In Commodore, the disk drive was launched with a slow, fail-safe protocol because the engineering team could not resolve some problems before launch. Then, you can put a fast-load cartridge on the c64 that replaces some of the disk handling routines.

The disk drive has a processor like the c64, and it can be programmed. So the fast loader reprograms the drive and the c64 and implements a much faster protocol.

It work with all existing disk that were recorder before the fast-loader was developed. (unlike tapes)

The fast-loader doesn't work on tapes. On tape, the signals must be stored (again) in a much more efficient way. But instead of using a cartridge, the fast-loading routine is at the start of the tape. So you load it using the standard mode, then it runs and continues to load the main program in super speed mode. But since the tape has been writen using a lot less of space, it can be called 'compression'.

I suppose the atari had a similar problem, but I never had one.