interest group vs social group

interest group and social group both are nouns.

Word	Noun	Adjective	Verb	Adverb
interest group	Yes	No	No	No
social group	Yes	No	No	No

As nouns, social group is a hypernym of interest group; that is, social group is a word with a broader meaning than interest group:

interest group: (usually plural) a social group whose members control some field of activity and who have common aims
social group: people sharing some social relation

interest group (noun)	social group (noun)
(usually plural) a social group whose members control some field of activity and who have common aims	people sharing some social relation