city vs city center

city and city center both are nouns.

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

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