The PBR book I linked above basically starts out by saying that PBR is ray tracing1.
No, they don't. pbrt is the name of the framework they walk you through in the book. You can find the accompanying source code here: https://github.com/mmp/pbrt-v3
The book walks you through the implementation of a ray tracing framework which uses physically based shading models. This doesn't mean that physically based shading is exclusive to ray tracing.
As mentioned before, physically based rendering is just an approach to shading and lighting with a foundation in the actual physics behind lighting and reflections, rather than working backwards from "what looks right" like we used to do in previous generations.