In general-
Compression - slowly lowers peak levels based on settings. More musical sounding.
Limiter - Hard wall at a certain level so no peaks are higher than the set level. Less musical sounding and more for protection from distortion.
Gate - Opposite of limiter. Only allows a signal to pass thru once it reaches a certain level. Usefull for drums so that only the drum being struck is passed thru instead of all the bleed from the other mics. Also usefull for wierd effects