I thought I was clear that path tracing and ray tracing shared similarities. But ultimately they differ in several key ways.
For example, ray tracing tends to be deterministic, and it starts at the view frame and moves toward the scene and then light sources. Path tracing has no such constraint. Modern path tracing techniques use a combination of ray-tracing-like paths as well as paths beginning from light sources (gathering rays and shooting rays, in the parlance of the field).
In principle you could consider path tracing to be some sort of specialized subset of ray tracing (or vice versa for that matter) but in practice it is different enough in its specifics and implications that it makes more sense to treat it as merely related.
For example, ray tracing tends to be deterministic, and it starts at the view frame and moves toward the scene and then light sources. Path tracing has no such constraint. Modern path tracing techniques use a combination of ray-tracing-like paths as well as paths beginning from light sources (gathering rays and shooting rays, in the parlance of the field).
In principle you could consider path tracing to be some sort of specialized subset of ray tracing (or vice versa for that matter) but in practice it is different enough in its specifics and implications that it makes more sense to treat it as merely related.