left brain vs hemisphere

left brain and hemisphere both are nouns.

Word	Noun	Adjective	Verb	Adverb
left brain	Yes	No	No	No
hemisphere	Yes	No	No	No

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

left brain: the cerebral hemisphere to the left of the corpus callosum that controls the right half of the body
hemisphere: either half of the cerebrum

Other hypernyms of left brain include cerebral hemisphere.

left brain (noun)	hemisphere (noun)
the cerebral hemisphere to the left of the corpus callosum that controls the right half of the body	either half of the cerebrum
	half of the terrestrial globe
	half of a sphere