A reciprocating air compressor works much like the engine in your car. An electric motor turns the crankshaft which causes the piston to rise & fall within the cylinder, compressing the air.
Rotary compressors use two precisely machined screws to continuously compress the air. Since the screws never change direction, there is less noise, heat & vbration than with a piston pump.
Another difference is that oil is used to seal the gaps between the rotary’s screws during compression while the reciprocating pumps have piston rings that will eventually wear out.
But what you really want to know is which one will work best for you. If you are a homeowner, hobbyist, or do-it-yourself type, then a reciprocating (piston) compressor will be ideal for you. A reciprocating compressor is not designed to run continuously, so we recommend sizing the CFM of the compressor about 1 1/2 times the required CFM of the air tool or equipment you're using. That will allow the compressor to cycle from time to time, and will help to prevent excessive wear and tear while keeping the pump cooled.
Rotary compressors are built to run continuously, producing a strong yet consistent airflow. So a rotary compressor is best if you are a commercial user and have a constant demand for air, but it will be a maintenance nightmare if it's cycled on and off too much.
To conclude, if you have a constant demand for air, pick a rotary screw compressor; but if your air usage is intermittent, then a reciprocating (piston) compressor is recommended.