brain surgeon vs sawbones

brain surgeon and sawbones both are nouns.

Word	Noun	Adjective	Verb	Adverb
brain surgeon	Yes	No	No	No
sawbones	Yes	No	No	No

As nouns, sawbones is a hypernym of brain surgeon; that is, sawbones is a word with a broader meaning than brain surgeon:

brain surgeon: someone who does surgery on the nervous system (especially the brain)
sawbones: a physician who specializes in surgery

Other hypernyms of brain surgeon include operating surgeon, surgeon.

brain surgeon (noun)	sawbones (noun)
someone who does surgery on the nervous system (especially the brain)	a physician who specializes in surgery