In common usage and in NFA regulations (I think) but the actual law (Title 18 section 921 (a) (6)) defines the "less than 26" overall" weapon as a short barreled shotgun.
Personally, I like the AOW designation better anyway, because it is only a $5.00 SOT, and I've always wanted a pistol grip sawed off side by side, like some redneck moonshiner from hell might have. When I find a Stevens or a Stoeger for cheap enough, I'm going to have one made.