Led Zeppelin’s “Carouselambra” from In From the Out Door. It starts out as a fast hard rock song, has a sludgy middle part, and ends with an odd synth/disco section from minute 7 to the end of the song (over ten minutes). I still am not sure whether this song is a forgotten epic…or the worst thing Led Zeppelin ever did.
So, in your view, Led Zeppelin’s Heartbreaker/Living Loving Maid (She’s Just a Woman) should also qualify as one song? In fact, there’s probably a stronger argument for those two songs really being one since radio stations almost always play them together.
Incidentally, they broke up the Heartbreaker/Living Loving Maid combo in the Led Zeppelin box set. A lot of fans absolutely hated that.
Estranged by Guns N’ Roses comes to mind.
The melody and chords change drastically halfway through the song.
Coma might also qualify though the different part could be considered a very long outro.
(For that reason I’m not listing November Rain)
Jim Croce Dreamin Again the last chorus is slowed down, I think to give it a reflective emotion.
Another like that is “Won’t You Try?/Saturday Afternoon” from Jefferson Airplane’s “After Bating at Baxter’s”. Not only is there no gap between them, but lyrical motifs from the first are repeated in the second (and vice-versa IIRC), clearly making it one song. Nevertheless, the “Saturday Afternoon” part has a different tune and a distinctly different tempo from “Won’t You Try?”, so I think it fits the thread theme.
I have also just thought of much better known example of a song which is listed as two songs, each of which sounds distinctly different, but has no clear gap, and where the whole (the two taken together), is clearly greatly artistically superior to the sum of the parts: “Brain Damage/Eclipse” from The Dark Side of the Moon. As a work of art, this is a single song that changes completely (both musically and lyrically) part way through.
These are not just “commonly played back to back”, separating them ruins both parts.