Sauron is one of the Maiar
, an order of divine beings. He is something like a fallen angel. Five of the Maiar were sent to Middle-earth in human form to oppose Sauron, and they became the "Istari". Tolkien uses the word 'wizard' to specifically refer to the five Istari, but to be fair he also did occasionally refer to the magic of both Elves and Sauron as "wizardry". This is all taken from the Silmarillion
Regarding the original query: as Denethor said, Gandalf is a wanderer: "Many are my names in many countries, he said. Mithrandir among the Elves ..."
(Mithrandir = "grey wanderer"). Tolkien once specifially referred to Gandalf as "Odinic", given that Odin was often seen as an enigmatic wanderer in a blue cloak.