Most NY permits are restricted to “Target and Hunting” or “Present Employment” or “Premises”. It sucks, but it is what it is.
Hence “Unrestricted” may mean something different here.
Very much so. In most States (WV, for example), there's no such thing as a permit to own a gun. If I want to buy a gun at retail I go to the gun shop, pay, file a 4473, pass the NICS, and take it home. Carrying openly is legal. The (unconstitutional) law requires a permit to carry concealed. This last item is what I'm calling a "restriction".