Sausage on bread is what it’s called, we’d never call that a hotdog.

And fairy bread is just fairy bread, you’re not putting two slices together.

I think that makes sense. I suspect you probably wouldn't call a bacon butty/bap/roll a burger either. Same for pani ca meusa, torta, and cemita.

Basically the Aussies picked up burger as from American influence, changed the meaning, then decided that the yanks defined it wrong. Meanwhile all the other bun based sandwiches get to keep the meaning. That said... the international chains haven't helped the matter.