So any helo the President is on is "Marine One". It used to be that the Army (Army One) and Marines took turns, but not for a couple of decades.
Any Air Force plane that the Prez is on is Air Force One. And when Bush took that Navy plane to the aircraft carrier for his codpiece fashion show, that S-3 was called "Navy One". Currently it is the only "Navy One" ever to exist, and has been retired and put in a naval museum in Pensacola.
I remember when this happened the Democrats were very critical of the PR stunt, calling it a re-election photo op and wanting to know why they went through the extra expense of using a Navy anti-submarine jet instead of simply using Marine One.
The Bush campaign defended the stunt, saying that the per-hour costs of the S-3 and Marine One were comperable. They didn't say anything about the cost of replacing Navy One when it was retired (spiffy new paint job and all) two months later and put in the musuem in Pensacola. I guessing quite a few million dollars.