The term "Paradox" is a Holland and Holland trade mark, other makers have different names for the same type of barrel.

There is also such a thing as a "ball" gun. Having true cylinder smooth bores intended to fire a round ball fitted to the bores. I have seen such a gun, a 12 ga double, fitted with rifle sights and stocked like a rifle.

Now days we have slug barrels, often rifled. There is a rumor that Bernardelli made a double barreled slug gun in recent times.