Pumps provide head to the fluid so that it can be transferred from one place to another. It does not pressurize the fluid, It simply transfers momentum. It is used for liquids as well as gases at low pressure and high volume.
Compressor: as the name suggests,it has the ability to compress gas and then the valve opens to deliver the gas at that pressure. It is used for gases at high pressure and low volumes such that it pressurizes the gas inside the device body. It provides pressure energy to the fluid.
Thus every compressor is a pump but every pump is not a compressor.