urban center vs city

urban center and city both are nouns.

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

As nouns, urban center and city are synonyms defined as:

urban center and city: a large and densely populated urban area; may include several independent administrative districts

Other synonyms of urban center include metropolis.

urban center (noun)	city (noun)
a large and densely populated urban area; may include several independent administrative districts	people living in a large densely populated municipality
	a large and densely populated urban area; may include several independent administrative districts
	an incorporated administrative district established by state charter