I'm pretty sure they do get to decide if it is a mod app or admin app. And I think only Jailbreak gets mods so that is why there hasn't been alot of mod apps going up. *Someone correct me if I am wrong pls.*That is not a distinction you get to make.
EDIT: About your edit also, Jailbreak mods don't have to go help out in other servers, they only have mod powers in Jailbreak. *Again someone please correct me if I am wrong, this is all just from my understanding.*