chalcedony vs agate

chalcedony and agate both are nouns.

Word	Noun	Adjective	Verb	Adverb
chalcedony	Yes	No	No	No
agate	Yes	No	No	No

As nouns, agate is a hyponym of chalcedony; that is, agate is a word with a more specific, narrower meaning than chalcedony:

chalcedony: a milky or greyish translucent to transparent quartz
agate: an impure form of quartz consisting of banded chalcedony; used as a gemstone and for making mortars and pestles

Other hyponyms of chalcedony include bloodstone, heliotrope, carnelian, cornelian, chrysoprase, onyx, plasma, sard, sardine, sardius.

chalcedony (noun)	agate (noun)
a milky or greyish translucent to transparent quartz	an impure form of quartz consisting of banded chalcedony; used as a gemstone and for making mortars and pestles