farmer's market vs green market

farmer's market and green market both are nouns.

Word	Noun	Adjective	Verb	Adverb
farmer's market	Yes	No	No	No
green market	Yes	No	No	No

As nouns, farmer's market and green market are synonyms defined as:

farmer's market and green market: an open-air marketplace for farm products

Other synonyms of farmer's market include greenmarket.

farmer's market (noun)	green market (noun)
an open-air marketplace for farm products	an open-air marketplace for farm products