In both NY and NC :
- new plates : you must display both plates
- historic / year of truck plate/plates : you must display as required in your truck’s year
In NC you are issued two new plates. If you do not display them, and if you display year of manufacture plate/plates, you must carry the new plates in your cab and display them to police if you are stopped. There is no limitation on type of travel. You do not need to get annual inspections.
In NY you do not get new plates - you get a antique/historic vehicular registration. I think there were limitations on “type of travel”. You must get annual inspections.
Your state DMV should be able to tell you the rules. They might be on the DMV’s website.
Please correct me if I wrong about NY and/or NC.