C* and Nz control laws
They are quite different. C* is a blend of pitch rate (q) and Nz while Nz is just that, Nz - normal acceleration. I used C*, before somebody gave it a name, for the first fly-by-wire implementation on the F8 while I was at Draper Lab. We used the Apollo inertial systems initially as the primary sensors. Things have evolved a lot since those initial ventures. I used C* in NASA Space Shuttle control law studies as well, for atmospheric flight to landing.