i have a planing hull, which i guess is a carving hull? its flat bottom, ie not displacement.
Surf is pretty different to white water, skills are shared, but surf is much more predictable and easy to read. Rivers have water going every which way, if you drop the wrong edge at the wrong time you get flipped, which is the same in the surf, but picking which edge you should have up is obvious. Generally i find it a lot harder to stay upright on a "river" (penrith) wave, then a surf wave.
Its hard to explain the differences now i try, but i find rivers much more of an adventure, but surf is easier to find.