What is the difference between “Mechanical SHP” & “Thermodynamic SHP” ?

What is the difference between "Mechanical SHP" & "Thermodynamic SHP" ?

A Gas Turbine Engine (Turboshaft) may quote Mechanical SHP of 650 but a Thermoynamic SHP of 813

I’ve just learned something myself in the process of researching your answer. I’m not in this field so I haven’t really given it any thought before now.

The thermodynamic shp is an effective horsepower rating at operating altitude above sea level. The density of air affects the performance of gas turbine engines, therefore at take-off, the available horsepower from the engine is different than it is during flight. [1]