In VA its CHP (Concealed Handgun Permit). It covers concealed handguns only - no other weapons.
Many other concealed weapons are allowed also; but no registration, license, or permit is needed for these.
Open carry of handguns does not require any registration, license, or permit (with some restrictions).
In Georgia, it's a GFL (Georgia Firearms License). It's a license to carry a firearm on your person, OC or CC.
No difference. Every state has it's own lingo and way of saying the same thing. Montana is CWP, concealed weapon permit.