special interest group vs special-interest group

special interest group and special-interest group both are nouns.

Word	Noun	Adjective	Verb	Adverb
special interest group	Yes	No	No	No
special-interest group	Yes	No	No	No

As nouns, special interest group and special-interest group are synonyms defined as:

special interest group and special-interest group: an interest group that tries to influence legislators or bureaucrats to act in their favor, typically through lobbying

Other synonyms of special interest group include advocacy group, lobby, lobby group, pressure group, special interest, third house.

special interest group (noun)	special-interest group (noun)
an interest group that tries to influence legislators or bureaucrats to act in their favor, typically through lobbying	an interest group that tries to influence legislators or bureaucrats to act in their favor, typically through lobbying