Although stoner bands like Bongzilla, Electric Wizard, & Unearthly Trance, and the like are often misclassified as sludge, the similarities are primarily a matter of historic concept & some musical attitudes, but they sound distinct -- stoner metal tends to be more melodic, while one of the prime aesthetics of sludge is discordance -- in a Godflesh or Scorn, uncompromising sense.
It grew out of Lousiana in the early nineties, although it is remarkably similar to the Melvins' work prior to that, and there is a significant amount of influence. Though Flipper, Swans, Neurosis can be credited as the first proto-sludge bands, I would opine that EyeHateGod, Crowbar, & Buzzov*en were the earliest distinct bands (88-90). Acid Bath ('91) could also be credited as a sludge band, but I believe they are distinct, although having influenced & been influenced by the genre.
Soilent Green (formed '88) and Dystopia ('91) are the next bands on the family tree, and practiced a grind-influenced form of sludge that's best described as a cacophony of hatred & pop culture references, overladen with discordant bass lines and almost nulled-with-distortion guitar work, staples of sludge metal.
Cavity ('92) formed in Florida, and has broke up since ('03), but are notable for their relatively prolific number of works.
Iron Monkey emerged around '94, taking more influence from stoner music (melody), but I still believe their early work to fall into straight sludge. Rwake ('97) quickly became a very distinct sludge metal band, as much in their distorted, almost nihilistic music, as well as their lyrics & thematic elements.
I won't neglect the questionable Corrupted ('94), who many consider a more straight forward Funeral Doom style, or stoner. However, they have released a great number of records, both in Japan and abroad, especially as split 7" vinyls with other artists, and deserve a certain degree of consideration. As with Dystopia, Soilent Green, and Rwake, they play an extremely discordant music, seemingly only monotonous bass lines overladen with vehement amounts of feedback, whilst most of the vocals are grunting of one form or another, often for notably long periods, broken up by long instrumental sections.
The sound is one of the more vile I've heard in music (perhaps not in a bad way), and is definitely in direct competition with the screeching of black metal, although I haven't the time to get into as long lived a genre as BM. Sludge is, in short, exactly what it says -- slow moving, undeveloped, untreated sewage, flowing with hatred that only rotting in the deepest piles of excretion can produce, & full of misanthropy and self-hatred.