You are correct, ANY USAF plane carrying the President is Air Force One. Likewise, the Marine Helicopters carrying the President are Marine One. Any, I would assume similar for any Army or Navy flight carrying the President.
As for the Big Blue Bird, there are two of them. Tail Numbers 28000 and 29000. Details here at the White House. And more details at Boeing's AF1 site
I am endebted to the two of you (Salgak and deport; posts 38 and 41, respectively) for improving
on my recollection from watching a documentary on Air Force One.
I'm always learning at freerepublic.com.