An actuator combines a power source with something that moves. In nearly all modern robots this is an electric motor plus a gearbox that trades speed for torque, and an encoder that reports the resulting angle back to the controller.
Hydraulic actuators use pressurised oil and deliver very high force for their size, which is why they appeared in heavy construction machines and early jumping legged robots. Pneumatic actuators run on compressed air, are cheap and springy, and are common in simple grippers and factory clamps.
The choice shows up directly in a robot behaviour: a gripper driven by an air cylinder is either open or closed, while an electric gripper can stop at any width and control how hard it squeezes an egg.
