The early Despecialized were a mix of the 2006 GOUT edition upscaled to 720p and the bluray downscaled. The latest release has switched that over to 35 mm film scans instead of the 2006 GOUT. The next step is to make it full 1080p.
Then there are he 35 mm preservations. Currently we have the Star Wars SSE, the TESB grindhouse and the ROTJ grindhouse. A grindhouse edition is not fully cleaned up. More cleaned up versions are in the works, but nothing final yet.
Several attempts have been made to clean and enhance the 2006 GOUT (which stands for George’s Original Unaltered Trilogy and usually specifically refers to the 2006 DVD bonus disc with the original films).
Preservations of older laserdisc editions are out there. There was the Faces edition in 1995, the Definitive Edition in 1993, the Special Widescreen Edition in the late 80’s, the Japanese Special Collection at about the same time. Most of the older versions are pan and scan and of limited interest. There is a bootleg from back in the early 80’s that Moth3r archived that is probably the earliest version of the film. Then there is Puggo’s 16 mm preservation (Puggo Grand aka ANH, Puggo Strikes Back aka TESB, and Return of the Pug aka ROTJ which is still forthcoming).
There are also project working on the 97 SE, and the blu-ray.