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Hi! Simply, compressor converts electrical energy energy into mecanical energy . The electrical energy is consummed by an engine whereas the mechanical energy is given into compressing air and rising its pressure.
Turbines receive mechanical energy in different forms ( gas, compressed air, circulating water...) and convert it also to mechanical energy.
A goog example is the turbo compressor or turbocharger of cars: hot pressurised air comes from the exhauster and rotates the turbine, which, linked to a compressor, makes it turn at high speed. The commpressor feed the engine with high air flow rate.