All the names Beretta quotes are indeed just various different names for the same round.
not ever to be confused with any of the approximately half dozen other types of 9mm ammo.
in north america, you will almost always see the one you refer to being called 9mm parabellum(latin, meaning"for war"), or 9mm luger, on cartridge head stamps.
if you are using older 9mm pistols(except the hearty but aged browning high power!), its best to avoid military surplus ammo, as it tends to have been meant for smg's, and could be too hot for some frames to handle.