city limits vs city

city limits and city both are nouns.

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

city limits (noun)	city (noun)
the limits of the area occupied by a city or town	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