Solidsheep,
It is important to understand that in the United States legal authority for crimes is invested in BOTH the states (each of which may have somewhat different laws) and in the Federal government. Most firearms regulations remains at the state level, although the US Government can -- and does -- have several overriding statutes regarding firearms.
Let me try to make this complex subject a little simpler, with the following illustration concerning the possession of jacketed hollow point handgun (JHP) cartridges (and, please note that I am NOT an attorney, so this illustration is designed to distinguish between state and federal jurisdiction, not to provide definitive legal information):
a) In Virginia, it is legal for most citizens to possess JHP ammunition (state law with no superseding Federal statute).
b) In New Jersey, it is illegal for most citizens to possess JHP ammunition under many circumstances (state law with no superseding Federal statute).
c) Federal law allows citizens to transport JHP ammunition (and handguns) through New Jersey, by complying with several detailed requirements delineated in Title 18, United States Code.
Therefore, if I were driving from Virginia to New Hampshire:
a) It would be legal for me to drive in Virginia with a box of JHP cartridges in my car’s glove compartment (Virginia law).
b) However, it would be illegal for me to do so in New Jersey (New Jersey law).
c) Unless I did so in ways that specifically complied with the Federal Law, therefore protecting me from New Jersey prosecution.
This is a difficult and complex area, particularly for Europeans raised in societies where criminal law is ONLY authorized at the national-level. I hope this simple explanation is useful.