Rednecks can live anywhere in the rural south. Hillbillies live only in the mountains of Appalachia.
"Hillbilly" tends to be associated with a lot more naivete than "redneck", because it's presumed that hillbillies live in remote areas. And I'd say that hillbilly is a lot more offensive than redneck.
You'll note that redneck, according to Peaches-n-Cream's definition, is associated with a working-class farm laborer, most definately NOT a yeoman or someone who owns their own farm. This is why my family never considered ourselves rednecks. In today's world, many former tenant farmers or farm laborers now own their own farms and have reclaimed "redneck" as a term of pride, much like many other formerly derogatory terms. Of course, these same farm workers now often discriminate against Latino farm laborers.
I could really write an essay on all this stuff.