metropolis vs inner city

metropolis and inner city both are nouns.

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

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