left hemisphere vs left brain

left hemisphere and left brain both are nouns.

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

As nouns, left hemisphere and left brain are synonyms defined as:

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

left hemisphere (noun)	left brain (noun)
the cerebral hemisphere to the left of the corpus callosum that controls the right half of the body	the cerebral hemisphere to the left of the corpus callosum that controls the right half of the body