child care vs day care

child care and day care both are nouns.

Word	Noun	Adjective	Verb	Adverb
child care	Yes	No	No	No
day care	Yes	No	No	No

As nouns, day care is a hyponym of child care; that is, day care is a word with a more specific, narrower meaning than child care:

Other hyponyms of child care include daycare.

child care (noun)	day care (noun)
a service involving care for other people's children	childcare during the day while parents work