nuclear family vs household

nuclear family and household both are nouns.

Word	Noun	Adjective	Verb	Adverb
nuclear family	Yes	No	No	No
household	Yes	No	No	No

As nouns, household is a hypernym of nuclear family; that is, household is a word with a broader meaning than nuclear family:

nuclear family: a family consisting of parents and their children and grandparents of a marital partner
household: a social unit living together

Other hypernyms of nuclear family include family, home, house, menage.

nuclear family (noun)	household (noun)
a family consisting of parents and their children and grandparents of a marital partner	a social unit living together