The terms "bronze" and "brass" are fairly ancient words that have long since lost their original metalurgical meaning. Originally, a copper based alloy that contained zinc was called brass, while a copper based alloy that contained tin was called bronze. Today, there are hundreds of copper based alloys that contain zinc, tin, lead, silicon, nickel, aluminum, and God knows what else. Each alloy is tailored for a certain combination of strength, ductility, machinability, corrosion resistance, cost, etc... Any of these products can be marketed as Brass, Bronze, Copper Alloy, Gilding Metal, etc...
As far as your gun barrel and firing chamber are concerned, there is no difference between any of these copper based alloys.