Read this very informative.
Here's an extract
With mechanical supercharging, the combustion air is compressed by a compressor driven directly by the engine. However, the power output increase is partly lost due to the parasitic losses from driving the compressor. The power to drive a mechanical turbocharger is up to 15 % of the engine output. Therefore, fuel consumption is higher when compared with a naturally aspirated engine with the same power output.
Exhaust gas turbocharging
In exhaust gas turbocharging, some of the exhaust gas energy, which would normally be wasted, is used to drive a turbine. Mounted on the same shaft as the turbine is a compressor which draws in the combustion air, compresses it, and then supplies it to the engine. There is no mechanical coupling to the engine.