There seems to be a jurisdictional escape clause in the sense that possession without use within the US without the intent to attack aircraft may not fall into interstate commerce. In which case the state law would govern the act.
Note they started adding the "interstate commerce" in there after the first version of the gun-free school zone act was found unconstitutional. Which then continued on to do the exact same thing when amended.
It's a distinction without difference.
Post Wickard v Filburn, mere possession of something has been found to be interstate commerce even if it's just a plant grown on your own property for your own consumption without ever entering interstate commerce. Note the controlled substance act depends on the same interstate commerce clause but they've upheld federal convictions for simple possession without showing any actual effect to commerce -- instead arguing that they've influenced interstate commerce by deciding to not participate in it and that if people did that in aggregate it would affect interstate commerce therefore it is interstate commerce. Complete madness obviously, but that's where we are.
"In Lopez, the Court held that while Congress had broad lawmaking authority under the Commerce Clause, the power was limited and did not extend so far from "commerce" as to authorize the regulation of the carrying of handguns, especially when there was no evidence that carrying them affected the economy on a massive scale. (In a later case, United States v. Morrison, the Court ruled in 2000 that Congress could not make such laws even when there was evidence of aggregate effect.)"
IANAL