From Tolkien Gateway

Wasn't Thuringwethil a skin-changer, too? And Sauron, who took the shape of a wolf? Mll 18:02, 30 October 2019 (UTC)

I think here that Skin-changers refer more to races outside of those who never had a completely defined form. Thuringwethil never is completely defined as any race other than a Vampire, so I'm not entirely certain about her, but Sauron is a Maia and therefore can take any shape he wishes if he wants a physical body (at least before the Ring's destruction incapacitated him too badly to ever be able to take a form again). Maiar and skin-changers are distinct from one another; I'm personally not sure which one Thuringwethil was but she could have been either. --Holdwine Meriadoc (Talk/Contribs/Edits)