I know goth (the subculture, which is distinct from "gothic architecture") has many meanings to many different people, but they all go through Siouxsie Sioux, Ian Curtis and that subculture in late 70s UK. It seems like that's what we're talking about here, too.

Manson came later & certainly drew influence from there in addition to glam and, probably most heavily, industrial metal. Avril Lavigne was a Canadian pop star who drew from the pop-punk aesthetic. She wasn't goth at all.