Airport: A place often with multiple runways where commercial aircraft regularly take off and land usually based on a schedule, it has buildings for passengers flight management (Control tower) and services such as refueling, maintenance etc. An airport is normally a commercial enterprise.
An Airfield is on a much smaller scale usually non commercial and used for private or irregular charter flights minimal runways and limited services can also be military. minimal if any control.
An Aerodrome is an old English word that has been replace with the word airfield so aerodrome and airfield are the same.