Its actually been a bit of a process. First I thought I had discovered an alternate matte painting used for the 81 release. Then I realised it was the same as the 77 painting. Then I thought the 81 release was the same painting from 77. Then I once again thought they redid the matte painting in 1981. Then I thought maybe the foreign--french/german--releases had a different matte painting. Its been a very tricky process of changing my conclusion as new pieces of evidence become available.
I've worked with
1) all the screenshots in the screenshot thread of the shot, notably the SE, GOUT, Moth3r, Citizen and Cowclops shots
2) my own screenshots from the HD-SE, GOUT, plus my VHS and my Editdroid LD rip just for the heck of it
3) a photograph of the movie screen of this actual shot from a 1977 screening
4) a medium-quality reproduction of the matte painting itself taken from the Lucasfilm Archives book
5) high-res scan of a 16mm print of the shot from Zion's 1977 print
6) low quality reproductions of the raw matte composite
I have done extensive graphic manipulation to reveal that:
drumroll....
There is no "alternate" matte painting or alternate moon. Both the 1981 shot and the 1977 shot are the same. If you look at Cowclops, Editdroid, pretty much any 1981 version, the moon doesn't look very different from the GOUT/SE, other than massive detail loss and wildly fluxuating colors. The only version that looks different is the Moth3r/Citizen PAL versions. This is why I wondered if maybe there was an alternate matte used for the foreign version. But I've always noticed that Tatooine was exactly the same, just cropped, and the contrast areas on the moon match up if you look at distinctive areas, although in some areas its tenuous--did a hypothetical alternate matte artists try to replicate the look of the original? No, I realised. It IS the original.
Explanations:
1) why is it that the Moth3r/Citizen French/German captures look different? They do indeed look different. There are four reasons for this. 1) as detailed as they are, they lack the fine detail of the GOUT/SE. None of the LD captures have sufficient detail to reveal the craters and cracks that are visible on the GOUT and SE, not even Moth3r's. Yet Moth3r/Citizen's still are clearly different looking from the other R1 captures, which have even less detail. This is because 2) contrast/brightness. This is why the atmosphere haze matte line and dark side of the moon matte line are visible. This matte line visibility is seen in some of the R1 caps as well, which causes the landscape/detail of the moon to change. This is why some of the R1 caps sorta look like they might be the same moon as the R2, but not entirely. I imagine this was a home video thing. 3) cropping. If you look at the R2 Moth3r/Citizen versions, most shots have some cropping compared to other versions, but this Tatooine shot is massively zoomed in, and this also contributes to the feeling that the shot is different. But then, even when we account for these three combined factors, and play around with the levels in photoshop to equalise all the versions, the Moth3r/Citizen caps still don't quite match up--they begin to resemble the R1 caps and the GOUT/SE caps, enough to make you consider that they may all be the same matte painting, but not entirely, because they are still not 100% identical. This is because of a final, crucial factor:
4) distortion. The actual matte painting that McQuarrie painting was very large, much larger than what is scene--yet it had to be framed and photographed within a 35mm 2.35 aspect ratio. When it was photographed, there was too much headroom--Tatooine only occuped a small section of the bottom frame. When it came time to do the final composite, it was vertically stretched to fill more room on the frame. Haven't you noticed that the moon in the GOUT/SE/original prints is so distorted? It looks eliptical. The R2 Moth3r/Citizen caps are simply the undistored, original composite, although it has additional cropping as most shots in this print do. This, I argue, is because the shot was re-composited for the foreign French/German prints because of the foreign crawls. They composited it without vertically stretching the Tatooine/Moon matte.
I'm going to do a graphic-heavy analysis of this so people can see for themselves, because they probably don't entirely believe me. I'm not 100% on this yet--but I'm 99% that this is the explanation.
EDIT
Further revelations on the 77 comp: it appears it was manipulated far more than we may have imagined. Each planetoid--Tattoine and its two moons--seem to have been isolated in three matting stages and each one manipulated as a seperate element and then re-composited with the starfield and ship models. This is concluded by comparing the raw matte element to the final optical composite. 1) The colors have been shifted on all three elements. Tatooine has been darkened and has more blue in it, while the moons have been rendered black and white from their original pale reddish color. This may be why the moons appear blue, green and grey in various prints/transfers, due to recompositing in 1981 and for foreign re-comps. 2) after being broken up into three seperate elements, each one has been repositioned! Tatooine remains as it was, basically, while the large moon has been moved higher in the frame and slightly to the left, and the small moon has been moved way higher and slightly to the right. 3) Theres been distortion applied on top of this. The small moon has been left as is, but the large moon has been stretched vertically. Additionally, it appears Tatooine may have been stretched horizontally, though it is a bit difficult to tell.
This is why, on some of the artificially brightened home video captures like Moth3r's, there are matte lines around the large moon (VERY visible on its darkside) and the atmosphere haze on Tatooine--even though it was painted as one matte painting, it was recomposited as seperate elements!
Reading The Making of Star Wars, there was two starfield passes done because Lucas didn't like the first one. This may be where the other 1981 starfield came from. Interesting.