Allow me to clarify things a bit further.
A shotgun is a shoulder-fired, smooth-bore weapon, with an overall length of 26" or greater, with a barrel length of 18" or greater.
A short-barrel shotgun (SBS) is a shoulder-fired, smooth-bore weapon with an overall length less than 26" OR a barrel length less than 18".
A rifle is a shoulder-fired weapon with a rifled barrel, with an overall length of 26" or greater, with a barrel length of 16" or greater.
A short-barrel rifle (SBR) is a shoulder-fired weapon with a rifled barrel, with an overall length less than 26" OR a barrel less than 16".
An Any Other Weapon (AOW) is a loop-hole category in the National Firearms Act of 1934. It is a catch-all for weapons that don't fit the descriptions of either a rifle, shotgun, handgun, machinegun, Destructive Device, SBR, SBS, or suppressor. It can include a litany of things, to include (but not limited to):
pen guns, cane guns, firearms with both rifle AND shotgun barrels between 12-14", smooth-bore handguns, handguns with a forward grip that extends below the bore axis.
For instance, my company manufactures an AOW based on the Remington 870 reciever. The recievers have never had a shoulder stock attached to them, meaning they have never been intended to be fired from the shoulder. The reciever is mated to an 11 7/8" barrel, and rear pistol grip. Since they are built as a smooth-bore, hand-fired weapon, they are categorized as AOW's.