I don't think these explanations are quite right. Some cities have an ICAO (organisation that dispenses airport and airline codes, amongst other things) "city code" as well as an airport code. London is LON, New York is NYC, Tokyo is TYO, Paris is PAR. This is usually the case where there is more than one airport. I think the new airport at Denver is DIA - I think I've seen it on luggage labels. DEN is probably the generic code for the city. There are cities with just one active airport that have seperate airport and city codes - Osake is OSA, but the airport is KIX.
fly Saha Air 707s daily from Tehran's downtown Mehrabad to Mashhad, Kish Island and Ahwaz