Most of the words in use actually do have very specific meanings. Automatic and revolver are not exclusive categories. One refers to the mechanism, and the other to a function of the mechanism in loading and firing rounds.
However, over time the usage of words tends to change in order to highlight the significant changes or divisions in technology of the day. Hence rifle originally referred to the specific feature found inside the barrel, but over time came to refer to all longarms which were not shotguns, because it was broadly assumed they were rifled and because they usually used rifle cartridges.
The point of rifling in a barrel is to make the bullet spin along its axis. This has a significant effect on the accuracy of the bullet.
If a non-spinning projectile is traveling along, any slight deviation in the direction it is traveling will add up and make the projectile move relatively far from its line of fire. This can result in what is known in shooting circles as a “miss”.
But if the projectile is spinning, the deviation doesn’t matter very much. The deviation is one direction in relation to the projectile and when the projectile spins, that deviation ends up moving the projectile in every different direction as it travels. And this means all of the movements cancel each other out and the projectile ends up traveling relatively straight along its line of fire.
In the US, the ATF has the final word. And the answer is ¯\(ツ)/¯
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.
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.
@Alessan has the closest answer, but there are brass cased shotgun shells. I don’t know whether smooth.
@TriPolar the Taurus Judge that shoots either .45 Colt or .410 bore has traditional rifling, though it’s shallower than traditional. The best pic I can find
The reason rifled shotguns exist is mainly because of Midwest hunting laws. Probably because the ground is flat and populations can be dense they want to limit the distance a slug can travel, but rifling is more accurate. Now some states are allowing straight-walled cartridge rifles for hunting.
Just to add to any confusion, in the last couple of years a “new” type of firearm has been marketed. It fires shotgun shells, either shot or slugs. It has a 14" more or less barrel. It’s not a shotgun, nor a short barreled shotgun. It’s a firearm and transfers on the 4473 as “other”.
It’s not a shotgun because the shotgun definition says “means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder”. This firearm has a “shockwave grip” and not shoulder stock. In effect it’s a short barreled shotgun, but does not require NFA registration nor a $200 tax.