I don't know if there's a specific technical term for it. If I was talking to other songwriters (in my local songwriters' group, or an online community I use) we'd just say something like "variant chorus," "alternative chorus" or "modified chorus."
Singer-songwriters and bands who write their own material don't seem to bother much with standardised technical terms for this kind of stuff. If they need to clarify the structure, they can just play the relevant bit. But the "hit factory" songwriters who create songs for major pop acts may well have additional technical terms to help them discuss the song structure with micromanaging producers. You don't find them slumming it with us amateurs and semi-pros, so I wouldn't know.
It's even more confusing when you try to talk about a second, completely different section of music that's also being used as a chorus. In my notes, I'd call it "chorus 2," "chorus B" or "alternative chorus," but talking to someone else it'd take me a whole sentence to clarify that no, I don't just mean the second time the chorus is played. And yes, the phrase "alternative chorus" can cause confusion with the situation you were describing. It really is that vague!
_________________
You're so vain
I bet you think this sig is about you