If we see Br2 in a post, we know it's two atoms of bromine (Br) that are "hooked" together. It's a diatomic molecule of bromine, and it is representative of bromine gas as we encounter it. The Br2 here is bromine gas.
Br2O3, as a compound, is an annhydrous, neutral molecule that is the most likely thermodynamic product of bromine oxoacids left to sit for an indefinite amount of time. In its most stable conformation, it resembles bromous acid, but an additional bromine replaces the hydrogen atom.
Barium Bromide
Dibromine Pentoxide
Diboron Heptoxide