Artscroll calls one "gold", the other "fine gold." Any other distinctions?
Well, Ibn Ezra (to Songs 5:10) says that paz actually means "precious stones." Rashi seems to agree, because he explains זהב מופז (I Kings 10:18) as meaning that "it gleams like a pearl", and in Daniel 10:5 he also says that כתם אופז means "an arrangement of pearls."
Radak on the verse in Kings brings three possible translations for מופז: refined (i.e. "made into paz"); a placename (i.e., "from Ufaz" - compare Jer. 10:9); or simply "good gold" (Targum Yonasan). (Lehavdil, Strong's concordance derives מופז and פז from an assumed root פזז, "to separate, to distinguish.")
So according to this view, paz indeed means refined gold, as opposed to zahav which is just the generic term for the metal.