BP means "Black Powder".
I'm not sure about Arizona laws, because they're all different. That's what you will need to check.
In California, I can mail-order a BP firearm, etc. For the purposes of commerce, background checks, etc., it's legally a non-gun, like you said.
HOWEVER, the laws about carrying a gun are completely separate. They have their own definitions of "firearm" and "loaded". For the purposes of carry, a "firearm" is anything that fires a bullet by means of an explosive propellant. So, as soon as I load a BP revolver, the same laws apply to it as would apply to a cartridge gun. (Loaded, however, in California, means "loaded and capped." If you take the caps off, it's not legally loaded.)
ADDITIONALLY, the Fish and Game Code has some different definitions, particularly WRT the definition of "loaded firearm", and "in a vehicle."
Now Arizona's laws are different. But they could be written in many ways.
Check them!
Just know that the Federal "non-gun" definition does not necessarily apply to loaded carry, either open or concealed.