The delta blues refers to the blues that comes from the Mississippi Delta (which I have driven through.)
Most of the best delta music came out during the depression. Robert Johnson, Blind Lemon Jefferson even Muddy Waters all come from the delta. The so called Chicago blues was mainly electric delta music. The sounds of the delta are superficially similar to Lightning Hopkins and other Texas blues musicians.
Delta blues songs are never straight (or almost never) 12 bar blues. Allthough when it reached Chicago the blues started to become more structured, mainly because in Chicago most of the musicians had to play more with bands. In the delta most blues musicians played by themselves, and thus the guitar and the voice became intertwined.
Interestingly the delta was still very much the same way it was in the 20's and 30's up to the 70's. And even now there are many blues musicians who sound like the delta blues men. There is something about the delta which is creepy, particularly if you drive through in the night (which we did). We also listened to Robert Johnson at the same time, and boy was that a wierd experience. To really understand the delta blues one must go to the delta and see it.
Robert Johnson: King of the Delta Blues
The Best of Muddy Waters (Any one of them, there's one recently released that has Waters' early Chess recordings, which are his delta blues stuff, and there are some things with his Library of Congress recordings. His electric stuff was really electric delta blues.)