However typically in video game rendering, ray casting refers to the specific technique where you only trace rays against a 2D scene for a single scan-line, and then draw the entire column of pixels based on that result, such as is done in Wolfenstein.

Ray-Tracing really can be used for anything that intersects rays against a scene but is typically used for set of techniques that at-least involve sending out primary rays from the camera via ray-tracing, but with "ray-tracing" GPUs we are seeing it used more specifically for secondary rays coming from the Camera.

"path-tracing" is generally the set of techniques that end up with a full path from camera to light.

Now, there isn't really much in rendering that sends out rays only from the light source, it's still just too computationally impractical.

However, there is "bidirectional path-tracing" which generally sends out rays from both the camera and the light source, then tries to join them in the middle. It's a bit more complicated but generally converges quicker than other montecarlo renderers.

Anyways, as I said, it's a big mess, partially because it's a big continuum, and there are generally renderers that exhibit properties from multiple of these categories.