The current Air Force One is a 747-200, actually; and yes, it's a *lot* bigger than a 757.
Air Force One is the designation of any plane the president is aboard. The main presidential transport is the 747, but he occasionally takes other craft if he's going somewhere with a short runway -- I think the backup is a 727 or 737.
As far as I know, the planes Cabinet secretaries use for official travel aren't assigned to them 365 days a year -- they use one from the pool of VIP transports.