Piston compressors are operated by crankshaft with lots of moving parts inside the machine, whereas screw compressors are operated by 2 two meshing helical screws.
The main difference is in their use. Screw compressors are usually bigger and used for heavy duty tasks. However, although screw compressors are more expensive to buy than piston compressors they can save you a lot of money on energy costs. This is because screw compressors often offer variable speed options which means they can automatically regulate the power and pressure needed for the tasks you are undertaking. They can also shut themselves off when not being used meaning you could save a lot of money on electricity bills.