In New York state there is a difference between "historical" plates and "vintage" plates (see links at bottom). North Carolina has different rules and procedures.
Also, in NY you have to have an inspection every year; buy, in NC there is no inspection after registration.
I have done one vintage plate in-person at the Albany, NY DMV office and one by mail (sent in a color photograph) and one at my local/main DMV office (Troy, NY DMV). I could not use my local/town DMV office.
In both states: If the year of your vehicle only had one plate, you can use one plate. If the year of you vehicle had two plates, you must have both plates.
In NY, if you take your vehicle off the road (and/or let registration lapse), you must send your plate to a DMV office for "storage".