I've never heard of a gun with smooth bore in one barrel and a rifled choke in the other. If it's a SxS with a gauge sized smooth bore on one side and a caliber sized fully rifled barrel on the other, it's a cape gun.

The Paradox type guns were intended to use a brass case loaded with a true bullet sized to match the bore rather than a slug. In other words a gauge sized rifle cartridge. Not a shotgun cartridge loaded with a slug. Modern shotgun cartridges loaded with a slug will have an undersized slug to avoid trouble going through a choke. A 12 gauge slug load will typically have a 14 gauge sized slug. There are modern slug guns with a rifled choke and intened to take a shotgun cartridge loaded with a slug.

Where I'm at a gauge sized rifle or gauge sized rifled choke gun would be legal for deer while a regular centerfire rifle is not. (Never understood why. Never found any deer up in the tree tops. But I can legally hunt rabbits and squirrels with my 375 H&H.)