olfactory brain vs nerve center

olfactory brain and nerve center both are nouns.

Word	Noun	Adjective	Verb	Adverb
olfactory brain	Yes	No	No	No
nerve center	Yes	No	No	No

As nouns, nerve center is a hypernym of olfactory brain; that is, nerve center is a word with a broader meaning than olfactory brain:

olfactory brain: a center in the cerebral hemispheres that governs the sense of smell in lower animals; in humans it seems to mediate complex emotional behavior
nerve center: a cluster of nerve cells governing a specific bodily process

Other hypernyms of olfactory brain include center, centre, nerve centre.

olfactory brain (noun)	nerve center (noun)
a center in the cerebral hemispheres that governs the sense of smell in lower animals; in humans it seems to mediate complex emotional behavior	a cluster of nerve cells governing a specific bodily process
	a center that provides information and control