For Arizona, plates are plates. The sticker on the plate is what distinguishes, to the police, what the registration is. The state has normal-use, emissions-area registration, out-of-emissions-area registration (ie, don't live in or commute into PHX or Tucson), and collector's registration. One can get collector's insurance on any type, but for collector's registration (which allows one to be emissions exempt) one must show proof of collector's insurance.
So, I could get the copper Historic Vehicle plates on my '78 Chrysler or on my '86 Trans Am and still use either for daily drivers so long as they're registered as normal emissions-area registrations. I could also put collector's insurance on those cars and still have them registered normally, the only penalty would be no coverage by the insurance company if I were caught, like after an accident.