I had a nosey through the CVP manual. It does seem to be using a slightly different approach, with "Left / Main / Layer" voices as opposed to L / R1 / R2 / R3. It also does group "voice" and "style" on separate pages when displaying registration contents. So I agree Mike - it would be sensible to be able to save Left independently of style on S / Tyros / Genos, but you can't.
Anyway, though, what was most interesting to me as I looked through the manual (for the first time) was that a lot of the screen layouts - especially the mixing console - actually look very much like the Genos screens. I suppose the CVP was the first arranger-style keyboard to use a touch screen, so they've reused the look and feel. I had just assumed the Genos screens were all new.