Hydraulics and Pneumatics are two major ways of fluid power application. Hydraulics deals with the use of pressurized liquid to generate control and transmit power, while pneumatic is branches of physics that deal with the use of air i.e., nitrogen or compressed air, to generate, control, and transmit power.
Due to the fact that liquids usually maintain free surface, and they usually tend to have higher mass compared to gases, they are incompressible under hydraulics. In pneumatics, on the other hand, gases can be easily compressed due to the fact that they don't maintain a free surface, plus they don't usually have a very high mass.
Hydraulic systems are mostly used to generate power when high force is required, although the systems might be moving very slowly. However, pneumatic systems are mostly used to generate power when little force is required, and they tend to have faster motion compared to hydraulic systems.