Drum Machine Designer is only available for electronic styes of music, correct?
Correct when working with Drummer. But you could create a software instrument track, choose Drum Machine Designer from the Instrument slot and use it for whatever genre you'd like, programming MIDI as usual.
Otherwise, Drum Kit Designer is used?
For Drummer tracks, yes.
Would you mind explaining the difference between the two?
Basically Drum Kit Designer emulates a real acoustic drum kit, whereas Drum Machine Designer emulates electronic drum machines. You choose one or the other depending on the style you're after, for example for 80s pop rock you may want a drum machine, but for blues rock you'd choose a drum kit.