parasol mushroom vs agaric

parasol mushroom and agaric both are nouns.

Word	Noun	Adjective	Verb	Adverb
parasol mushroom	Yes	No	No	No
agaric	Yes	No	No	No

As nouns, agaric is a hypernym of parasol mushroom; that is, agaric is a word with a broader meaning than parasol mushroom:

parasol mushroom: edible long-stalked mushroom with white flesh and gills and spores; found in open woodlands in autumn
agaric: a saprophytic fungus of the order Agaricales having an umbrellalike cap with gills on the underside

parasol mushroom (noun)	agaric (noun)
edible long-stalked mushroom with white flesh and gills and spores; found in open woodlands in autumn	a saprophytic fungus of the order Agaricales having an umbrellalike cap with gills on the underside
	fungus used in the preparation of punk for fuses