Pin is the Power which is entered into circuit.Pavs is Available Power from Source.
They are obviously different.If Pr is zero ( conjugate matching ) all power available from the source enters into circuit.
Re: Why does the available power equal abs(b)^2-abs(a)^2?
To start with we should clarify some terminology:
Pavs (aka the available, incident, exchangeable power from the source)=|a|²
Pr (reflected power)=|b|²
Pin (absorbed, transmitted, or actual power) =|a|²-|b|².
So the equation in the first attachment is fine: Pin=Pavs-Pr.
But the second attachment is completely off. I'm not even sure why the condition ΓL=ΓS* is relevant. That doesn't have anything to do with conjugate match condition...