witch doctor vs thaumaturgist

witch doctor and thaumaturgist both are nouns.

Word	Noun	Adjective	Verb	Adverb
witch doctor	Yes	No	No	No
thaumaturgist	Yes	No	No	No

As nouns, thaumaturgist is a hypernym of witch doctor; that is, thaumaturgist is a word with a broader meaning than witch doctor:

Other hypernyms of witch doctor include magician, necromancer, sorcerer, thaumaturge, wizard.

witch doctor (noun)	thaumaturgist (noun)
someone who is believed to heal through magical powers	one who practices magic or sorcery