It's a little of both.
The National firearms act requires registration and a $200 tax on any title 2 weapons. This would include fully automatic weapons, short barreled rifles and shotguns, silencers and so on.
The Gun Control Act of 1968 banned the importation of "non sporting" weapons. and tightened a number of other unconstitutional controls on firearm ownership.
The Firearm Owners' Protection Act of 86 banned the fed from accepting new registrations of automatic weapons for civilians.
What the Veterans' Heritage Firearms Act would do is allow veterans or their families to register any title 2 weapons they may have by means of an amnesty. They would be treated as if they had been in compliance all along.
Right now, if they're caught, they're prosecuted and their historical firearm is seized and most likely destroyed.