I believe that there WERE 100 other airborne divisions in the past, they just do not exist anymore. World War II required a lot of divisions airborne or otherwise.
Later on, existing divisions were designated according to type. Infantry is the 'default' designation. Cavalry units were designated, then Armor, then Airborne, and finally Mountain. I have no idea when Artillery got its own designation. Some units subsequently were designated Air Assault, and this includes the 101st, but it kept the Airborne title to honor the unit history.
Other branches have other policies, but this is how the Army structure evolved.