black wizard

[Earendilyon]

I believe actually that the term 'wizard' is exclusive to the group of Maiar that came to Middle Earth at the beginning of the Third Age at the bidding of the Valar. One would not consider Gandalf a Balrog, though Balrogs are a type of Maiar as well. The same would apply for calling Sauron a member of the Istari, or a wizard.

Sorry if I seem to nitpick here, but there were no specific "groups" of Maiar. All Maiar are Ainur and so they have the ability to take a physical shape (or stay in spirit form, like Gandalf/Olórin mostly was when he still was in Valinor). The Balrogs were Maiar who became evil and clothed themselves with a Balrog physical shape. The Istari (which just means 'wizard') took physical shape as human beings. Although they had different physical appearances, both Balrogs and Istari were Maiar.