What does make difference between a WTHD and a THD from practical point of view? Where and when the WTHD is more prevalent than THD?
Weighted THD is preferred over THD when an inverter is generating non-sinus waveforms. Take a BLDC machine, this is usually excited with a trapezoidal current waveform
THD aims to express the quality of a sinus so if what is being generated isn't a sinus its benefit of determining how pure the output waveform is (w.r.t. what it is expected to be) has been diminished.
WTHD aims to to predict the distortion in the current (and thus the additional losses)