Now in the episode Barney Gets His Man , at 13:40 in the episode you see a visual of the State Police's Police Car and The Mayberry Police Car. And they look almost exactly the same except for the writing on the car like "State Police or Mayberry Police". Am I right that they are almost a replica of each other or exactly the same??
That would be fairly normal, even today, because states often get 'deals' with a car maker to purchase all their police cars from that maker. That would mean that many police agencies from that state would end up having patrol cars that were very similar.
+1 what Floyd said.
These are likely 'Fleet' specials and / or 'Pursuit Vehicles", meaning souped up motors and tighter suspensions for the police market, be they state, county or municipal. They are otherwise stripped down of most creature comforts, but usually have higher out put alternators for generating electricity for the power hungry radios and such. As such they all were all basically the same shape, model and color to keep costs down. The motors were likely heavy duty (four bolt mains) big block V-8's with huge carburetors and / or super chargers... or turbos. This, in most cases made the pursuit vehicles faster than the civilian cars. DesiLu probably had several pursuit vehicles in their fleet for TAGS and other shows.
Another DesiLu offering, Sheriff of Cochise County/U.S. Marshal (1957-1960) made nearly exclusive use of Desotos. Desoto may have been a sponsor.