Air Force One is the designation call sign for any aircraft that is carrying the President of the US. When he departs the a/c and it flys away, that a/c then flies with a different designation.
There are currently two Boeing 747 aircraft that are painted in the colors and with the Presidential seal. The one carrying the President on board is commonly referred to as Air Force One (whichever of the two plane is in service).
Air Force Two is the a/c that is carrying the Vice President.
Marine One is the helicopter that flies the president to and from the White House lawn. Again, this designation is for the helicopter while the President is on board. The Marine squadron may have more than one configured to carry the President.
During times of war, the President is transferred to an E-4 Airborne Command Post. From this a/c, the President and staff can make decisions to go to war. This a/c was depicted in the movie "Patriot Games", and it had some good interior views of the aircraft layout.
There are 3 E-4 aircraft that are used for this mission. There are 4 other E-4's that are assigned for Air Force's mission to have a flying command post. These a/c can be rotated between the different mission requirements. Whenever, the President goes outside the US on Air Force One, the E-4 Command Post stays within 200 miles of his location in case an emergency developes.