theres open chords, which leave some played strings unfretted. these generally sound better with a clean sound (acoustic or electric, just not distorted)except for E and A which really are kind of like power chords
for distorted guitar barre chords sound 'better' to most. a power chord is a type of barre chord where you only play the root, the fifth, and the octave root of the chord. so it isnt major or minor and can be used in either context. but the most important thing about it is that only using the root and fifth creates better harmony when its distorted a lot.
you can play different types of barre chords other than a power chord. like major, minor, seventh, etc etc but again, while they sound better than open chords on a distorted guitar, they arent up to power chords level of 'rockness' if that makes sense hehe
if you wanna play rhythm just use less gain to make a kind of crunch sound (like jimi hendrix' tone or cleaner) and it will sound ok with open chords and the like...