I see a lot of bands have drumsets in which the drums seem a little smaller, maybe they are lower, do they have a name for those? And also I'm wondering if there are any cheap drum sets that have just a bass drum, hi hat, and snare?

smaller drums have a higher sound. I'm guessing you're talking about tom-toms? I'm sure if you looked you could find a kit with just those parts, but most would have at least one tom. Try 2nd hand ones maybe?
yeah I looked on MF, I'll try google. And I don't mean the toms, it just seems like the bass drum and maybe even the hihat is smaller
Jazz sets. No?

I saw the drummer in a blues band use one the other night, they're pretty cool.

My brother, (the drummer in our band) says they're jazz sets. Yeah.
if it is all smaller, it may just be a smaller scaled one, fusion sets have smaller toms and floor toms, (sometimes bass drum) but everything else is the same