Yeah, that's pretty much exactly wrong.
Path tracing exists not because it's faster (it isn't, except perhaps in some pathological conditions), it exists because there are certain lighting effects that standard recursive ray tracing doesn't handle at all, but path tracing does. Caustics, global illumination, subsurface scattering, etc... We could be using ray tracing for just about everything now, but we don't because it doesn't look very realistic.
(Photon mapping can be used to create those lighting effects as well, but path tracing seems to have won out, being a bit less fiddly. With photon mapping you have to know sort of what you're going to be looking at in advance, whereas with path tracing you don't.)
Path tracing can be very slow, but improvements in computation speed plus algorithmic tweaks to prune unnecessary work mean it can be sort of done in real time these days.
One of the big differences between ray tracing and path tracing is that the former is deterministic, whereas the latter is probabilistic. Ray tracing just does a bunch of math until it arrives at the answer, but in path tracing the image quality depends on how much effort you put into it. If you use a few rays per pixel, you get a grainy image. If you use a lot of rays per pixel, you get something that's a lot smoother and clearer, but takes a long time to render.
One of the big semi-recent advances is to use denoising algorithms. Instead of throwing a lot of compute cycles at the problem to trace lots of rays, you just render a noisy image and use some algorithm (perhaps based on machine learning, perhaps not) to smooth it out. So now instead of tracing 100 or 1000 rays per pixel to get something that looks good, you might only trace 10, or 2, or 1.