Not certain what the current legal term is...
Short Barrel Rifle
Stocked Pistol
Sawed off Shotgun / rifle
(legal) curio & relic?
and there is also the catch-all AOW (Any Other Weapon)
The fed moves guns in and out of these groups, seemingly at their whim.
Curio & Relic in particular has changed several times in the last few decades.
Essentially, (as I understand the law)
A Handgun has no buttstock, and a barrel length less than 16".
A Rifle has a buttstock and a barrel length 16" or more.
A shotgun has a buttstock and a barrel length of 18" or more.
There is also an overall minimum length requirement, as well.
(there are also exceptions, and it can get very confusing)
If it falls outside these boundaries, it is regulated by the ATF under the 1934 NFA.
You can have a handgun with NO barrel if you wish, but I wouldn't want to be the test case, should the Fed decide that "no barrel = no rifling= sawed off shotgun".