I believe the "path tracing" you described here is actual path tracing insofar each sample is one "path" rather than one "ray", where a "path" does at least one bounce, which is equivalent to at least two rays per sample. Though I think the "old" path tracing algorithm was indeed very slow, because it sent out samples in random directions, whereas modern path tracing uses the ReSTIR algorithm, which does something called importance sampling, which is a lot faster.

The other significant part is that path tracing is independent of the number of light sources, which isn't the case for some of the classical ray traced effects you mention ("direct shadows" vs path traced direct lighting).

That's at least what I understand of the matter.