Hi Keith,
Please could you clear up some doubts in my mind?
The first type is THP which is used to push the aircraft forward against the drag.
I thought we simply called that "thrust"?
The second type is the power that is wasted in propelling the propwash rearwards.
I thought that is how we generate thrust - by accelerating a mass of air backwards - why would it be considered wasted if it generates something useful?
The only waste I can see is considering all of this with the brakes on, so there is no useful acceleration of the aircraft.