"Air Force One" isn't technically a plane: It's simply the radio call name for any U.S. Air Force plane carrying the president of the United States.
As soon as the president steps aboard an Air Force plane, that plane is referred to as Air Force One by the crew and all air traffic controllers, in order to avoid confusion with any other planes in the area.
If the president rides on an Army aircraft, that aircraft is Army One, and whenever he boards his specialized helicopter, that craft is Marine One.