These are the skyways.
I came into the thread to mention “Destroyer.” Also, “Don’t” from Phobia reuses the tune from “Lost and Found” from Think Visual; and that album’s title track reuses the verses from “Definite Maybe” on State of Confusion. The Kinks catalog is full of songs that sound strikingly similar to earlier tracks.
I think you’re right.
In the Twin Cities, a lot of buildings are connected by corridors above the streets, kind of like indoor bridges. They’re there so you don’t have to walk around outside as much when it’s cold (and yes, I have seen bums up there during the winter). Those are skyways. He’s singing about that, not the type of thing that Disneyland used to have.
I think the song is about how every day when he walks on the streets he sees a girl up in a skyway but he can’t talk to her because she’s however many feet up indoors while he’s outside on the ground. Then one day he takes the skyway and sees her out on the street walking by his usual bus stop, but he can’t reach her.
So it’s really a song about isolation and alienation. Very well done, IMO.
The White Stripes’ “There’s No Home For You Here” from Elephant is pretty much the exact same song as “Dead Leaves and the Dirty Ground” from their earlier album White Blood Cells. Except in this case, the copy was an improvement, IMO.
Come to think of it, there are several early White Stripes songs that sound alike. Jack White’s songwriting ability has improved by leaps and bounds since their first album. *Get Behind Me Satan * sounds almost nothing like their debut, and not much like anything else either. I can’t wait for *Icky Thump * (despite the rather off-putting name).
The Jam had two songs with the exact same tune, both of which I really like. They can be found together on the album “Extras”, which is a compilation of B-sides and demos.
“Tales from the Riverbank” is slow and dreamy, and is the one that was released on an actual album.
*It’s mixed with happiness - it’s mixed with tears
Both life a death are carried in this stream
That open space you could run for miles
Now you don’t get so many to the pound
True it’s a dream mixed with nostalgia
But it’s a dream that I’ll always hang on to
That I’ll always run to
Won’t you join me by the riverbank*
“We’ve Only Started” is a fast paced rock song.
*Let’s take a chance with beginner’s luck
We have nothing so there’s nothing to lose
I can’t believe the only reasons we’re here
Are the reasons in the Bank of England
Hear me now
We’ve only started
They’ll just exploit us but it’s only day one
We haven’t got that far
Not far at all*
Ever see Bob Dylan in concert? New lyrics to old songs, often better than the originals. 
Elvis Costello–who discards more good tunes before breakfast than most songwriters can come up with in a lifetime–frequently takes a song idea and develops it into multiple fully relaized songs before settling on a final version. His working drafts, or alternate realizations of ideas that later turned up elsewhere, sometimes appear as B-sides or CD bonus tracks, providing a fascinating insight into his creative process. For example, there’s “Big Sister,” which has most of the same lyrics as “Big Sister’s Clothes” but a different chorus and a very different arrangement; there’s “American Without Tears No. 2,” which has the same melody as “American Without Tears” but a different feel and almost completely different lyrics except for the tagline; and there’s “Twenty-Five to Twelve,” which evolved into “Seconds of Pleasure,” which in turn contributed lyrics to both “Invisible Man” and “Love Went Mad.”
Don’t forget that REM did an alternate vocal track to Seven Chinese Brothers called Voice of Harold. As far as I can tell, it was just Michael Stipe reading the liner notes to a gospel album that was hanging around the studio. It’s still oddly compelling…
Pete Townsend used a bit of “Pure and Easy” in “The Song is Over”, though at that point I don’t think “Pure and Easy” had been released (or was intended to be released).
50s/60s song writer/singer Neil Sadaka released the same song twice. In the early 60s he sang Breakin’ up Is Hard to Do in his rock n’ roll style. In the late 60s/early 70s, he released the same song as a ballad. Both times it made the top 20 or so.
Along the same lines; Guns N Roses did two versions of “Don’t Cry” that were identical bar the lyrics.
Probably not what the OP was looking for, but Eric Clapton did an acoustic interpretation of Layla on his Unplugged album that almost constituted a rewriting.