city vs down town

city and down town both are nouns.

Word	Noun	Adjective	Verb	Adverb
city	Yes	No	No	No
down town	Yes	No	No	No

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