According to Chambers:-
Air'field: an open expanse where aircraft may land and take off
a'erodrome: an area, with its bulidings etc used for the take off and landing of aircraft
Air'port: an aerodrome, usu with a custom-house, used as a station for transport of passengers and cargo; an opening for the passage of air.
Hope this helps.
(god I must be bored
)
FWyg