urban center vs inner city

urban center and inner city both are nouns.

Word	Noun	Adjective	Verb	Adverb
urban center	Yes	No	No	No
inner city	Yes	No	No	No

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