The first model you describe is a subtractive model.
Conceptionally you start with white (paper) and subtract single rgb-components (which means you always keep two components).
Your base colours are cyan (blue+green, removes red), magenta (blue+red, removed green) and yellow (green+red, removes blue) plus black (for eficiency reasons) - so you can think of it as working with negative rgb-colours.
You can, of course, convert from cymk to rgb (but in practice it never really works since there's no 100% pure ink nor paper).
The colour-wheel is identical for both (the base-colours are just rotated by 60deg), "mixing" colours just works differently.
Traditionally artists pick colours from a palette (wheel) and adjust saturation/brightness with black & white - which is equivalent to the
hsv model.