inner city vs metropolis

inner city and metropolis both are nouns.

Word	Noun	Adjective	Verb	Adverb
inner city	Yes	No	No	No
metropolis	Yes	No	No	No

inner city (noun)	metropolis (noun)
the older and more populated and (usually) poorer central section of a city	people living in a large densely populated municipality
	a large and densely populated urban area; may include several independent administrative districts