They are giving u a fbi background ck and the firearm itself
What exactly does registering a firearm mean? Do background checks automatically register a firearm? Is it mandatory for a firearm to be registered? Here in the USA
Laws vary by state. Generally the background check does not register you. That is backwards. Applying to register a gun at purchase will trigger a background check. If you pass you are allowed to have the gun and the gun will be registered. Some states just require a background check without registering a gun.