lobby group vs interest group

lobby group and interest group both are nouns.

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

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

lobby group: an interest group that tries to influence legislators or bureaucrats to act in their favor, typically through lobbying
interest group: (usually plural) a social group whose members control some field of activity and who have common aims

Other hypernyms of lobby group include interest, political entity, political unit.

lobby group (noun)	interest group (noun)
an interest group that tries to influence legislators or bureaucrats to act in their favor, typically through lobbying	(usually plural) a social group whose members control some field of activity and who have common aims