city vs city centre

city and city centre both are nouns.

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

city (noun)	city centre (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