Barrel Interchangability Winchester/FN

Given the magazine tube ring and chamber length are correct, will a barrel meant for a FN shotgun fit onto a Winchester 1300 or 1200? I know the 1200 and 1300 barrels are interchangeable, so no question there.

I hear people say that FN shotguns are essentially just Winchesters with a different logo. If that is the case, FN barrels should fit onto a Winchester receiver, correct?

I ordered up a barrel. I'll keep you all posted as to whether it works or not.