It's always referred to support for specific relationships, as far as I've ever known. It's much more commonly used in book and television fandom. Fleetwood Mac is just so darn special like that.
Go to fanfiction.net comments sections if you want to see it used all the time.
I've actually never much cared about the L/S relationship dynamic. I've sort of taken it as just an interesting piece of trivia, and thought it was too bad that it's always made their collaborations a bit turbulent. The fact that people consider it a "mythology" is fascinating to me.
It would be great if Christine sang more than Don't Stop, but it would undoubtedly be other songs that involved the touring members of the band. Songbird seems unlikely, however lovely it is.