just offering an example for others, O Little Town of Bethlehem is sung to a very different tune in the US and UK. we’ve got both versions in MusicBrainz here:
I don’t know that we need a work type for both, but at the very least new relationships might be good. I know we’ve currently got “Quotes music/lyrics from”, but to my understanding these are for short quotations, not the whole song. there’s also “Is based on”, but that seems a bit too generic sometimes. this could also cover things like Ariana Grande’s 7 rings, which is largely to the tune of My Favorite Things from The Sound of Music.
I can already see a “To the tune of” relationship, but I don’t have an idea for the lyrical version of this relationship…