Offensive military airports are used for the military air transport units, while the normal (non-military) airports are used for air transport corporations, and I think vacation corporations
Here is something that I learned from hard experience. The Air transport corps in my empire were so profitable that I bought a couple with my CEO. Be careful doing that. When a new player takes over the country and messes up the work force, you have to live with it, because you can't move them.