What's the difference between physically based rendering and global illumination?
The two terms are, in a sense, orthogonal.

Global illumination refers to any process which simulates indirect lighting. Indirect lighting occurs when light bounces off surfaces or through media. The opposite of global illumination is local illumination, where only illumination directly from light sources is taken into account.

Physically-based rendering is a loosely-defined term, but the general idea is to model lighting, surfaces, and media in a way that is physically plausible. This includes, for example, ensuring conservation of energy, so that the solution to the light transport equations don't blow up.

Generally speaking, PBR can be thought of as a type of GI, but this isn't always the case; it's possible to use physically-based rendering without trying to solve the whole rendering equation. Moreover, PBR doesn't always try to model light exactly; quantum mechanical phenomena such as coherence and polarisation aren't commonly modelled (or are only coarsely modelled) in typical rendering methods.