family vs man and wife

family and man and wife both are nouns.

Word	Noun	Adjective	Verb	Adverb
family	Yes	No	No	No
man and wife	Yes	No	No	No

As nouns, man and wife is a hyponym of family; that is, man and wife is a word with a more specific, narrower meaning than family:

Other hyponyms of family include couple, match, mates, marriage, married couple.

family (noun)	man and wife (noun)
primary social group; parents and children	two people who are married to each other
people descended from a common ancestor
a social unit living together
(biology) a taxonomic group containing one or more genera
a collection of things sharing a common attribute
an association of people who share common beliefs or activities
a loose affiliation of gangsters in charge of organized criminal activities
a person having kinship with another or others