The way I understand it, natural harmonics at the the harmonics you find over an octave scale with a full scale length i.e. with no note fretted. these occur above the 12 , 5 and 7th (to name only a few).

Artificial harmonics are produced by winding up your gain (increasing the sensitivity of the amp) and finding the harmonics over a now different (shorter) scale length which results form fretting a note.

Im sure there are better definitions out there but this one works for me.

Natural = no note fretted

Artificial = note fretted