Faun, incubus, and satyr?

According to the Malleus Maleficarum, the faun, incubus, pan, and satyr are different names for the same demon. Medieval Christianity demonized the image of the rustic god Pan, which inspired the popular depiction of the devil with goat features. In fantasy gaming, the incubus and satyr are depicted distinctly (the faun is rarely depicted separately from the satyr, and the pan is nonexistent).

I think a way to represent this in fantasy gaming would be if the incubus monster was created from the faun or satyr by some means. Perhaps a faun or satyr who turns evil becomes an incubus, or vice versa? There are any number of ways to represent this transformation.