It's like the military then. The fact that there is a 101st airborne division does not imply the existence of 100 other airborne divisions.
Edit: Haha, went and checked. Damn the lying documentary I watched.
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.