Wow and flutter are usually measured by recording a single frequency tone from a test record and looking at variation of the frequency. This can be influenced by any eccentricity in the test record, or slack between pin and hole, although this is arguably still valid as it represents an issue common to all records. The frequency of change can give indications of the cause such as eccentricity on the platter, on the motor, or something belt or roller related. There are other methods like optical sensors and slotted or strobe discs, or more recently using accelerometers and/or gyros to measure rate of change of speed.
There are a couple of threads regarding cartridge measurements, how they are taken and what they mean:
https://www.audiosciencereview.com/...-cartridge-response-measurement-script.41148/ - details of a script used for analysis of frequency sweeps, including differences found between sweeps on different test records
https://www.audiosciencereview.com/...he-phono-cartridge-measurement-library.46108/ - results of this analysis for a range of cartridges, including tests of the same cartridge under different conditions, and of different examples of the same cartridge model giving some idea of sample to sample variations.