city center vs city

city center and city both are nouns.

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

city center (noun)	city (noun)
the central part of a city	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