Songs that evolved into other songs

Something like that. Although, to the best of my knowledge, Peel never mixed vodka with RockStar energy drink.

Another Yardbirds/Led Zep example - the guitar solo (starting at 1:58) in the Yardbirds' "Think About It" was later recycled in its entirety for "Dazed and Confused":

https://www.youtube.com/watch?v=UseyCdGNfaY

Here are the Yardbirds performing "Dazed and Confused" in 1968:

https://www.youtube.com/watch?v=AYDhx_DgDxE

... and of course <i>that</i> song was merely a cover of this 1967 recording (the audio is awful on the Youtube post, with the classic descending bassline almost inaudible, but you can get the gist of it):

https://www.youtube.com/watch?v=pTsvs-pAGDc

and obv large swaths of hip-hop and rap samples or borrows from older songs

Stephen Stills took his Buffalo Springfield song "Questions" and made it the second half of the CSNY track "Carry On":

https://www.youtube.com/watch?v=zDjmmCvTH7o

Meanwhile Neil Young took his own (albeit unissued at the time) Springfield track "Down Down Down" and--after adding new lyrics--incorporated it into his CSNY jam suite "Country Girl":

https://www.youtube.com/watch?v=lgw9R2kzG3Q

The Monkees "Goin' Down" started out as the backing tracks for an intended cover of Mose Allison's "Parchman Farm," then they decided to write their own song on top of it instead.

Siouxsie & the Banshees "Peek-a-Boo" was built upon sections of the horns and drum tracks played backwards from their cover of John Cale's "Gun."

Wilco did Outtasite (Outtamind) and Outtamind (Outtasite) (I may have sic'd these titles slightly) on Being There.

"Revolution 9" developed out of the last eight minutes of the 20 minutes jam on "Revolution 1".

hey hey my my -> my my hey hey

Any reason why the song credits be different?

The title track on The Police's Reggatta de Blanc came from an extended jam they used to do live during the middle-eight of 'Can't Stand Losing You'.

I think they never stopped doing that middle bit, live.

One peel session had it as titled "the missing bit from the middle of "Can't Stand Losing You""

Ha!

Phish did this a bunch, mostly due to things evolving through live performance. The one I remember is the end section of "The Curtain With" evolving into "Rift".

Bob Pollard has reworked older songs countless times:

Wall and Windows became Hardcore UFOs
Crocker's Favorite Song > Class Clown Spots A Ufo
Tell Me > Tractor Rape Chain
Superwhore > The Who Vs. Porky Pig
Girl From The Sun > Do The Collapse
Reptilian Beauty Secrets > Idiot Princess
Sacred Space > Office of Hearts
Rocket Head > Teenage FBI
many more...