I plan to measure Motor Drive signals with a TPS2024. Cat II & Cat III confuse me. What exactly is this?

CAT ratings are industry-standard category safety ratings, Test instruments are rated on their ability to withstand a voltage spike which are applied through a specified level of resistance.

The installation categories are:
CAT III Distribution-level mains (usually permanently connected). Equipment at this level is typically in a fixed industrial locations.

CAT II Local-level mains (wall sockets). Equipment at this level includes appliances, portable tools, and similar products. Equipment is usually cord-connected.

CAT I Secondary (signal level) or battery operated circuits of electronic equipment.