What's the difference in Biblical Hebrew between "zahav" and "paz"? 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.
Gold makes sense because its targum is sometimes דהבא and biblically it is paralleled by זהב, by כתם, and by חרוץ, along with other classical contexts where alternative translation is impossible, as the phrase פעמני פז. Evidence for "refined" comes from the parallel of 2 Chronicles 9:17 "ויצפהו זהב טהור" and 1 Kings 10:18 "ויצפהו זהב מופז" (targum דהבא טבא) as well as the Greek translation δόκιµος refined. However, ben Sira parallels it with the gemstones פנינים and ברקת and b. Yoma 44b has "זָהָב מוּפָז שֶׁדּוֹמֶה לְפָז" which suggests they are not to be conflated; Rashi there comments that a פז is a pearl, but, in addition to evidence from parallels, the Biblical+classical phrases כלי פז, עטרת פז, etc. demand a material of which tools or vessels can be formed. לבושי פז and ביגדי פז in Sidrei Avodah l'Yom Kippur allow for gold but not pearls. y. Yoma 23a quotes two alternative translations of the obviously related מופז, an adjective used to describe gold in 1 Kings 10:18. "מופז רבי פטרוקי אחוה דרבי דרוסא בשם רבי בא בר בינה דומה לאש מצתת בגפרית אמר רבי אבין לשם מקומו הוא נקרא זהב מאופז." Rabbi Patricius the brother of Rabbi Drosa in the name of Rabbi Abba b. Binah says that it is "Like fire kindled with sulphur;" i.e. blue (green and red gold are also discussed in Judaic sources) or dancing. The Semitic root פזז meaning dance is found in Biblical Hebrew, Arabic, etc. Rabbi Abin says it is formed by lenition of an א, for "from Uphaz," to which a second witness is MT Jeremiah 10:9's "זָהָב֙ מֵֽאוּפָ֔ז". Daniel 10:5's "כֶ֥תֶם אוּפָֽז" is a confirmation of the original א and a a weak challenge to the proper-noun theory and the vocalization of MT Jeremiah 10:9, though the Bible several times mentions כֶ֣תֶם אוֹפִֽיר, gold of Ophir. An alternative א-spelling doesn't conflict with Rabbi Patricius' position, however, because Breishis Rabbah spells the verb "אופזים" they danced. Abin and the Jeremiah vocalizer appear to be conflating זהב מאופז and זהב מאופיר (1 Kings 10:11), Ophir being a Biblical source of gold. TJ Jeremiah 10:9 reads "דַהֲבָא מֵאוֹפִיר" and Peshitta Jeremiah 10:9 has "ܕܗܒܐ ܡܢ ܐܘܦܝܪ," idem, but the three separate mentions and lectio suggests this is an emendation. The Peshitta has the same in 1 Kings 10:18. In part because the location of Ophir is completely unknown, we cannot reconstruct Uphaz as an alternative spelling.
In my opinion, the likeliest explanation is that the word פז refers to refined gold of quality good enough to be reflective when polished, so that it dances like flame when handled in light, a common metaphor in English as well. The connection to פזז dance is probably a folk etymology, though evidence of early association with a verb stem is found in מופז/מאופז, but it preserves the real meaning. Because פזז can also be spelled with an א and there was contamination from אופיר, it is not possible to reliably reconstruct whether "reflective/refined gold" or "gold from Ophir" was intended by אופז, by מאופז and by מופז, though my instinct is that the MT preserves the older version. The meaning of the b. Yoma is obscure and, looking at the parallel in y. Yoma, possibly itself confused. Ben Sira and early Jewish liturgy -- think מרשות הא-ל הגדול והנורא/ומרשות מפז ומפנינים יקרה With the permission of the Great and Wonderful God/And with the permission of He more precious than rubies and פז in the Simchat Torah blessings -- along with b. Yoma, may indicate a gemstone also called פז; however, almost all Biblical uses clearly refer to gold. The only possible exceptions IMO are SoS 5:15 and Lam. 4:2, and neither demands it.