red coral vs gorgonian coral

red coral and gorgonian coral both are nouns.

Word	Noun	Adjective	Verb	Adverb
red coral	Yes	No	No	No
gorgonian coral	Yes	No	No	No

As nouns, gorgonian coral is a hypernym of red coral; that is, gorgonian coral is a word with a broader meaning than red coral:

red coral: corals of especially the Mediterranean having pink or red color used for ornaments and jewelry
gorgonian coral: corals having a horny or calcareous branching skeleton

Other hypernyms of red coral include gorgonian.

red coral (noun)	gorgonian coral (noun)
corals of especially the Mediterranean having pink or red color used for ornaments and jewelry	corals having a horny or calcareous branching skeleton
the hard stony skeleton of a Mediterranean coral that has a delicate red or pink color and is used for jewelry