chill vs cool down

chill is a noun but cool down is not a noun.

Word	Noun	Adjective	Verb	Adverb
chill	Yes	No	Yes	No
cool down	No	No	Yes	No

As verbs, chill and cool down are synonyms defined as:

Other synonyms of chill include cool.

As verbs, chill and cool down are synonyms defined as:

Other synonyms of chill include cool.

chill (noun)	cool down (noun)
coldness due to a cold environment
a sudden numbing dread
an almost pleasurable sensation of fright
a sensation of cold that often marks the start of an infection and the development of a fever