family vs kin

family and kin both are nouns.

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

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

Other hypernyms of family include clan, kin group, kindred, kinship group, tribe.

As nouns, family and kin are synonyms defined as:

Other synonyms of family include kinsperson.

family (noun)	kin (noun)
primary social group; parents and children	group of people related by blood or marriage
people descended from a common ancestor	a person having kinship with another or others
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

family (adjective)	kin (adjective)
	related by blood