True, it doesn't. I didn't read the question carefully enough. Path-tracing is indeed a more sophisticated form of ray-tracing. In a path-tracing engine you'll still be calculating intersections to surfaces by ray-casting, ray-marching etc. As the wikipedia page for ray-tracing states, "ray tracing is a rendering technique for generating an image by tracing the path of light as pixels in an image plane and simulating the effects of its encounters with virtual objects". The range of complexity possible in that definition was already discussed in the above Quora article.

Yes. I wish there were more casual acceptance for “ray tracing” as essentially light computation via ray intersections, rather than the assumption that it means “naive ray tracing” or “direct lighting ray tracing”.

I feel like the first sentence of the top response answered the question in a way that is quite relevant to this discussion:

"Many people use the terms somewhat interchangeably."

That is true. If we want to discuss the differences, it's important to know that sometimes people are using two terms to discuss the same thing.

Right. The internet certainly has no shortage of folks willing to answer this question, but the answers almost always imply the difference is merely rhetorical or something like a matter of opinion. Same thing with ‘biased’ vs ‘unbiased’ rendering, but that one is much less surprising.