oyster fungus vs oyster mushroom

oyster fungus and oyster mushroom both are nouns.

Word	Noun	Adjective	Verb	Adverb
oyster fungus	Yes	No	No	No
oyster mushroom	Yes	No	No	No

As nouns, oyster fungus and oyster mushroom are synonyms defined as:

oyster fungus and oyster mushroom: edible agaric with a soft greyish cap growing in shelving masses on dead wood

Other synonyms of oyster fungus include oyster agaric, Pleurotus ostreatus.

oyster fungus (noun)	oyster mushroom (noun)
edible agaric with a soft greyish cap growing in shelving masses on dead wood	edible agaric with a soft greyish cap growing in shelving masses on dead wood