There are at least two “Air Force Ones.” The big one, a Boeing 747 requires a pretty long runway.
The smaller one, a 737, I think, is for shorter trips, or to airports with shorter runways, such as Latrobe.
Both have equivalent electronics, communications, etc.
The plane which the President currently occupies is designated “Air Force One.”
Yep even if he was in a Cesna it would be Air Force 1.