I live in Ohio and worked in Kentucky for almost 30 years. There is most certainly a "mountain" culture which I experienced by just crossing the Mason Dixon line every day when I took the bridge over the Ohio river. Thing is, to a large extent, even in a more "hillbilly" state, people are just people. Kentucky was, for the most part, like any more rural suburb of Cincinnati. That was true even though many people I worked with had been born in the mountains, many near or in Hazard.
There was, however, a significant minority which was different. It was the stereotype. As to them, I'll differentiate between "hillbillies" and "rednecks".
I like hillbillies, I think I'm a bit of a hillbilly myself. Someone who likes the country, likes DIY, and is far from pretentious. A redneck, however, is quite a bit more rowdy and more importantly, doesn't like non-rednecks.
Basically, the kind of cousin lovin' yahoo who gives respectable white trash like myself a bad name.
Intelligence is not a factor in either one. I've known some hillbillies who could crunch numbers in their head in ways to amaze me, although their speech was heavily accented and sounded like someone from "deliverance".
The difference might be that rednecks seem to be suspicious of and dislike people not like themselves whereas hillbillies are friendly folks who are nicer than many city folk I have known.
Again, both taken together were a minority, albeit a significant one. Mostly, people are the same all over.