In Japan they're called "Trainer's" instead of "Trainers." So Trainer's Item, Trainer's Supporter, Trainer's Stadium, and Trainer's Tool.
EDIT: Unless you meant why they're showing on those images. I guess they forgot to turn that layer off when exporting.
I've been calling them "galaxy" in my articles since 2003. I never saw anyone comment on that usage until this last year. But yes, they are interchangeable in the fandom since they have no official term (that I'm aware of). More than happy to revise my usage if/when we have an official term.