Inspired by this thread on bands that do songs with the same name as the band, the challenge here is to come up with cases where a group recorded an album and a song by the same name - but the song is not on the album.
I can think of exactly two examples:
The Doors - Waiting for the Sun Led Zeppelin - Houses of the Holy
Almost-example; The Who’s Face Dances didn’t have a title song on it, but a song by that name did appear on Townshend’s solo album All The Best Cowboys Have Chinese Eyes the next year.
Gomez’s “Bring It On” was on their second album “Liquid Skin”, not their first “Bring It On”. Also, “High On Liquid Skin” didn’t make an appearance on an album until they released the B-Sides album, “Abandoned Shopping Trolley Hotline”.
Several of the songs from the thread the OP linked to would qualify. For example, the song “They Might Be Giants” is not on They Might Be Giants’ first, self-titled album.
AC / DC = If You Want Blood; song on Highway to Hell, and a live album of the same name (“Ang-us! Ang-us!”)
I used that song to get psyched up for various things, even to take tests. In the obscure-but-interesting movie Empire Records (Liv Tyler, Robin Tunney, Renee Zellweger and a ton more people), Anthony LaPaglia as the owner of said record store retreats to his back office to play the drums and let off some steam to that track…
Kate Bush’s song “Never For Ever” didn’t appear on her album “Never For Ever.” In fact, it’s never appeared anywhere, but it’s known that she did record it.