What is the difference between a hydraulic clutch and a cable clutch?

Cable clutch - when you depress the clutch lever or pedal, you pull at a Cable whose other end is attached to the fork that operates the pressure plate in the clutch assembly.

Hydraulic clutch - when you depress the clutch lever or pedal, you push at a piston in a Master cylinder. Pushing at the piston pressurizes the hydraulic fluid in the master cylinder, and in the hose leading to a Slave cylinder placed at the clutch. The piston in the slave cylinder extends and operates the pressure plate in the clutch assembly.