Hi Mark,
I’m afraid you are misinformed, or maybe I misunderstand you.
Both Ray Tracing and Ray Casting ‘shoot’ rays from the Camera.
I am not exactly sure about Ray Casting, but I believe it is something like Rasterization.
Cycles is a Path Tracer and Ray Tracing is like a ‘faster version’ of Path Tracing. Path Tracing is the most realistic, but also the slowest method. Ray Tracing can get pretty close to Path Tracing in result, but is a lot faster.