Mechanical clutches use a cable for actuation(a clutch cable on the gearbox)and need to be adjusted every now and then depending on the clutch wear.
Mechanical clutches, just have a cable that connects the pedal to the gearbox.
Hydraulically actuated clutches are self-adjusting(just like disc brakes and drum brakes)Hence they need to be bled out just like the brake lines to make sure there are no air bubbles in the lines.
Hydraulic clutches require less effort to actuate.Hence heavier cars and 4x4 vehicles benefit from them.You don't need to adjust any cable depending on clutch wear.It is self adjusting.
Hydraulic clutches have a master and slave cylinder like a brake which will need to be replaced if it wears out.
Hydraulic clutches are more expensive on the whole because they contain so many parts that can wear out,plus the oil.You can use the same oil that is used in the brakes.Most DOT4 oils are brake/clutch fluid.Depends on what the car manufacturer has specified.
Common parts for both are a clutch disc,pressure plate,release bearing and flywheel.