All automatic weapons, silencers, and short barreled shotguns are banned. The only time a citizen may own a short barreled riffle is; if they are part of a recognized reenactment group, or if they are a curious and relics license holder. Large bore destructive devices and any other weapon (AOW) require a tax stamp from the ATF and proper approval, but are legal.
NFA weapons refer to a federal list of firearms that the government requires owners register. Not all states follow this law, and others have partial restrictions, full banns, or the need to register firearms in the NFA data base. Examples of firearms or other weaponry considered a NFA regulated weapon includes, but is not limited to: Machine guns, firearm suppressors, short barreled riffles and shot guns, and anti-tank guns (.50 caliber and up).