as far as I can tell "open c" was invented by slingshot in 2009 when they came out with the RPM. That year's RPM was halfway between a normal bridled kite and an actual C kite like the fuel, so they called it an "open c" because it's C shaped right but not entirely c shaped it's a bit flatter than that. But now I think when someone says "open c" what they really mean is a pure C shape with bridles? Who knows. Sure an "open c" can be a foil kite because as far as I can tell the only thing "open c" ever meant was that it was a marketing term. Correct me if I'm wrong. HQ kites have always had more of a C shape to them anyway. I don't really understand why HQ doesn't make their kites flatter so you get more performance from them. Anyway, that's my two cents.
Technically all kites are "ram air" as they use air pressure to support their shape, this includes inflatables. The difference is foils use it exclusively. That would differentiate ARCs by their use of spars and not their minimal bridle. Though sparred parafoils are still considered parafoils.
Bridled C kites are not a waste at all, by increasing the support the LE can be reduced in diameter. Then the speed is increased , weight reduced, balance improved, range increased and depower and power increased. It's like a win win win. For some reason , most likely incorrect info, kite designers get confused on the aerodynamic function of the tube and the amount of drag of a thinner tube vs some bridles and how to optimize bridle thickness to be structurally appropriate (hint they don't need to all be 4mm rope).
The reason bridles are so hated on C kites is it changes the feel, turns more pivot etc, and importantly tangles! If you are dropping kites lots bridles can become a real pain. A tangle on an inflatable can cause much more issues than on a foil, i.e. death loops etc.