black magic vs thaumaturgy

black magic and thaumaturgy both are nouns.

Word	Noun	Adjective	Verb	Adverb
black magic	Yes	No	No	No
thaumaturgy	Yes	No	No	No

As nouns, thaumaturgy is a hypernym of black magic; that is, thaumaturgy is a word with a broader meaning than black magic:

black magic: the belief in magical spells that harness occult forces or evil spirits to produce unnatural effects in the world
thaumaturgy: any art that invokes supernatural powers

Other hypernyms of black magic include magic.

black magic (noun)	thaumaturgy (noun)
the belief in magical spells that harness occult forces or evil spirits to produce unnatural effects in the world	an illusory feat; considered magical by naive observers
	any art that invokes supernatural powers