Most of the reruns I taped were pretty representative of the original show that aired, but when it turned out there was a big omission in the rerun, it could get pretty annoying. There are still a few holes in my collection that I haven't been able to fill just because rerun versions of SNL are so much easier to come by than original airings: by default, any episode aired after the live air date is the rerun version unless none exists (usually the weak and controversial shows would fall into this category).
Older reruns sometimes substituted bits for segments from other shows: a lot of material added to a rerun also appeared in a show without the rerun disclaimer; if a show without a disclaimer turned up in the rerun package, it usually meant the show was not repeated on NBC. Later reruns were a little more unusual in that the content that replaced what was cut didn't seem to be from any other episode. Sometimes it would be a live sketch done in the studio with the same host and cast, sometimes it would be a short film or commercial. One of these bits was actually the Roberto Benigni segment of Jim Jarmusch's "Coffee and Cigarettes".
The reruns from the last 25 years or so (from the point where Lorne Michaels returned to the show after his five-year hiatus) have some more subtle changes. Fans with sharper eyes and ears than mine had mentioned in various places online how the reruns sometimes replaced sketches from the live shows with performances from dress rehearsal. The differences were usually very minor, not really noticeable unless you made a point to look for them or if they made the change to remove something offensive. I did notice, though, the clock on the main stage with no other purpose but to show the time in the studio would sometimes visibly show it was a point earlier during the evening during monologues and musical guest introductions.
From what I guess, the strategy is to make the best possible rerun: if something went better in dress, then that's what they'll use. As well, because a new episode of SNL is live, it's more prone to technical screw-ups, miscues, and awkward "dead seconds"; reruns give a chance to fix some of that. The audio is also remixed a bit for the rerun, which often includes a faint bit of 'sweetening' to the audience response (just a few extra laughs mixed in).
I'd heard of all these things from different sources and noticed a few things here and there when I watched reruns of shows I'd seen when they aired live, but it didn't come together until the night I finally saw a recording of the live broadcast of the first show of 1985-86 hosted by Madonna. This episode is probably the most extensively edited SNL rerun; the most well-known change being that reruns remove the cold opening about Brandon Tartikoff getting urine samples from the cast for drug testing, giving the impression that the show just went straight into the opening montage. Other changes include a second Simple Minds musical performance added to the later part of the show, the replacement of the original Sarah Charlesworth "collage" opening montage with the filmed "limo ride" used from the fifth show of the season on (as well as all bumpers to keep consistent), dead seconds removed, hot mics were fixed, the Weekend Update title card was changed to the one used for the rest of the season, and Don Pardo's line "Two Junkies be located..." in a commercial parody was removed (probably for the same reason the drug testing had to be taken out).
There’s a podcast called The Loudest Girl In The World, hosted by Lauren Ober. The show concerns Ober’s autism diagnosis at 42, as well as her experience dealing with this information and opening up to others about it. When I listened to it last summer, I related pretty heavily to what she was talking about. I’ve also started to make peace with how my own brain works in the last few years. It’s been a rough road, though.