For firearms onboard in the various US states, the same exact rules apply as when transporting in any highway, etc. vehicle. You have to know the exact
rules for transporting firearms for each state you travel through.
If you are licensed to concealed carry in your home state, many other states will have 'reciprocity' with your home state ... its up to you to know exactly in which other state your home state CCL is honored, etc.
See: Concealed Carry Permit Reciprocity Maps - USA Carry
but such reciprocal agreement are changeable without notice.
If without a CCL, usually
you need to have the weapon locked in the trunk of the vehicle and the ammo lock/stored in an alternate location; no chambered rounds, no ammo in close proximity to the firearm, etc.
Each foreign government has its own statutes that must be precisely followed .... usually and varying from temporary confiscation until you leave the country to securing the firearm in a bonded 'safe' on board, etc.
Rarely will you be able to 'carry' when on foreign soil, even TO competitive shooting events.
It really isnt a big deal; but, your REALLY need to KNOW the laws where you travel .... like especially New York, and New Jersey, Wash DC, etc. .... and this does not include 'internet' information gained from a non-government website.
Travelling internationally on the oceans, international law plus the laws of the last country you visited and the next country on your itinerary will control some portion of the legal requirements. Do NOT depend on any foreign internet info for firearms entry; you want ONLY 'hard copy' (signed if possible) information from an embassy or consular office.