shaman vs medicine man

shaman and medicine man both are nouns.

Word	Noun	Adjective	Verb	Adverb
shaman	Yes	No	No	No
medicine man	Yes	No	No	No

As nouns, medicine man is a hyponym of shaman; that is, medicine man is a word with a more specific, narrower meaning than shaman:

shaman: in societies practicing shamanism: one acting as a medium between the visible and spirit worlds; practices sorcery for healing or divination
medicine man: a Native American shaman

shaman (noun)	medicine man (noun)
in societies practicing shamanism: one acting as a medium between the visible and spirit worlds; practices sorcery for healing or divination	a Native American shaman