No problem. Long pedantic answers on obscure topics are my specialty!
Both GOUT and theatrical refer to the unadulterated versions of the films. When films were released on home video, it was pretty typical for a few frames to get dropped, most typically at reel changes, but sometimes elsewhere. Honestly it’s not unusual for theatrical showings to also be missing frames at reel changes. Theatrical refers to that perfect set of every single frame ever on any projection prints. GOUT refers to a set of frames used by one of the most common, and most complete home video releases. Even when dealing with the exact same cut of a film, if you use a slightly different set of video frames, this affects sync, thus the terms “GOUT sync” and “theatrical sync”.
GOUT is a frame standard that dates from back when people were ripping Laserdiscs, based on the 1993 Definitive Collection Laserdiscs. These were re-released, with the crawl reverted to its original form, thirteen years later as a DVD bonus disc known around here as the GOUT. There were actually two GOUT standards, NTSC GOUT, and PAL GOUT, and they did not have exactly the same set of frames. If they don’t specify, people usually mean NTSC GOUT. There are nearly thirty years worth of synced audio and subtitles scattered over the Internet all using the GOUT standard, so if you just find some random Star Wars audio track, more likely than not, it’s GOUT-synced.
Theatrical is something we’re pretty sure about at this point, but technically we could still be surprised by an extra frame on some print floating around out there. Based on what we know right now, it goes like this:
Star Wars theatrical = NTSC/PAL GOUT + 1 extra frame
Empire theatrical = same as PAL GOUT, or NTSC GOUT + 2 extra frames
Jedi theatrical = NTSC GOUT + 2 frames, or PAL GOUT + 1 frame
Despecialized is GOUT-synced throughout, although the current Empire sync is off by one frame due to a mistake (if you add a one-frame offset to your audio/subtitle tracks, it goes back to perfect sync). 4K77 is GOUT-synced, and 4K83 is theatrically synced.
One frame is about 42ms, two frames is about 83ms – certainly the visuals from that number of frames are nothing you would notice was missing or not. And for subtitles, that amount of difference is irrelevant as well. Project Threepio is GOUT-synced, but it works fine with 4K83 with no modifications. Audio is another matter. A two-frame difference between audio and video is definitely something I can notice (and I was shocked to discover it’s bad enough I can notice it with dubs as well), but some don’t notice it at all. One frame is probably less than I could notice, but I’m sure others could.
In short, no matter which frame standard you use, you’re getting the original unadulterated cuts of the films. No special edition revisionist nonsense either way. But you can’t mix-and-match between the two standards haphazardly, or some percentage of the audience is going to think the audio’s annoyingly out of sync. IMO the main problem with trying to get people to change from GOUT to theatrical is that the standards are too close. If they were off by a full half-second or something, it would be clear when there was a mismatch. But as it stands, mismatched audio is just too easy to pass off as close enough.
The UHD/D+ versions are synced to some other Special Edition frame standard I don’t know anything about. If it’s not the original versions, I don’t really follow it.