Also, regardless of the NFA designation, suppressors are regulated as firearms under state law in many states, including Florida.
F.S. 790.001:
(6) “Firearm” means any weapon (including a starter gun) which will, is designed to, or may readily be converted to expel a projectile by the action of an explosive; the frame or receiver of any such weapon; any firearm muffler or firearm silencer; any destructive device; or any machine gun. The term “firearm” does not include an antique firearm unless the antique firearm is used in the commission of a crime.