Presumably, the difference between Rukia and Hitsugaya is that Rukia's dances do a direct temperature drop to freeze stuff, while Hitsugaya's manipulating water/ice (so, hydrokinesis? Aquakinesis?) to freeze stuff. I had to look up the Bleach wiki for this though, so grain of salt and all that.

I could not come up with a mechanical distinction between Matsumoto and Byakuya's, though.