Someone had this question a long time before you did, so the legal definitions already exist...

Gun Control Act Definitions

Shotgun

18 U.S.C., § 921(A)(5) and 27 CFR § 478.11

The term “Shotgun” means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder, and designed or redesigned and made or remade to use the energy of the explosive in a fixed shotgun shell to fire through a smooth bore either a number of ball shot or a single projectile for each single pull of the trigger.

ATF definition of Shotgun

Rifle

26 U.S.C., § 5485(a)

For the purposes of the National Firearms Act, the following definitions are used to define and verify the different types of firearms:
§ 5845(c) — The term “Rifle” means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder, and designed or redesigned and made or remade to use the energy of the explosive in a fixed metallic cartridge to fire only a single projectile through a rifled bore for each single pull of the trigger.

ATF definition of Rifle

Then beyond that, to alter a shotgun or rifle far enough to qualify it as the other (which actually usually ends up as an AOW, not a "rifle" or a "shotgun", or a "weapon made from a shotgun" or "wmfr") takes more than just replacing a barrel.

For example, putting a rifled barrel on an 870, does not constitute a rifle, because by definition, a shotgun is made to fire a number of shot OR a single projectile. With a rifled barrel, it is still capable of this.

Alternatively, firing birdshot loads out of a rifle, without altering the rifle, has not changed the rifle design, and therefore has not converted it to a shotgun. By it's design and function, the rifle still is meant to fire ONE projectile through its rifled bore, and to wit, the nature of the projectile, being comprised of multiple pellets, doesn't matter in the designation of the RIFLE.

Where things get really hairy are handguns. For example, the Taurus Judge MUST forever be classified as a .45 long colt handgun, even though it is designed to and capable of cross chambering .410 shotshells. They would never be able to release a .410 only version, as a 'shotgun handgun' constitutes an AOW.