But for a few notable exceptions, yes. Shotgun barrels under 18" are considered Short Barreled Shotguns and are regulated.
If it's chambered for 5.56 and the ammo is typical commercial ammo and not specifically loaded for that barrel length (almost a custom job, really), then, yes, you are right.
If it's chambered for something else, such as 300 AAC Blackout then it could change the applicability of the barrel length.
But it shouldn't be, imo. Ever see someone try to break clays with a 18" bbl Mossberg 500 Tactical? Ever try to do house clearing with a Remington 870 in the 30" barrel "dove gun" config?
Back in the bad ol' days, shotguns were more like Henry Ford's "you can have it in any color you want as long as it's black." But now we have more disposable income (as a society), vastly more options, and dramatically better technology in shotguns. It's entirely reasonable now for most people to be able to have separate shotguns for turkey, deer, dove, and home-defense.
Peace favor your sword,
Kirk