Neck profile and neck radius are different things, although both have to do with the neck (obviously).
Neck radius has to do with the amount of arch in the fretboard. Picture if the arch of the neck were extended until the two sides met and formed a circle. The radius of that circle is the neck radius.
In other words, a fretboard with a 12" neck radius will be flatter than one with a 9.5" radius.
Origiinally Fender used A, B, and C to designate nut width (1.5", 1.62" and 1.75" respectively). That terminology is no longer in widespread use, and the designations just refer to the shape of the back of the neck. A “C” neck will be oval shaped and a "modern C will be flatter.
There is more to it, but that’s the Reader’s Digest Condensed Version.