family vs mates

family and mates both are nouns.

Word	Noun	Adjective	Verb	Adverb
family	Yes	No	No	No
mates	Yes	No	No	No

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

Other hyponyms of family include couple, match, man and wife, marriage, married couple.

family (noun)	mates (noun)
primary social group; parents and children	a pair of people who live together
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