Fundamental power often referes to the desired signal produced by the device or system. For example, if you measure the mains of a US domestic power outlet, it would refer to a 60 Hz sine wave. Harmonic power is the distortion from the ideal sine wave. It comes as a result of a fourier distrubution of harmonic frequencies that make up the distortion.
However, if the system is designed to produce a wave other than a sine wave, then the harmonics may not be distortion, rather they are intentionally produced harmonics.