barrel cactus vs cactus

barrel cactus and cactus both are nouns.

Word	Noun	Adjective	Verb	Adverb
barrel cactus	Yes	No	No	No
cactus	Yes	No	No	No

As nouns, cactus is a hypernym of barrel cactus; that is, cactus is a word with a broader meaning than barrel cactus:

barrel cactus: a cactus of the genus Ferocactus: unbranched barrel-shaped cactus having deep ribs with numerous spines and usually large funnel-shaped flowers followed by dry fruits
cactus: any succulent plant of the family Cactaceae native chiefly to arid regions of the New World and usually having spines

As nouns, cactus is a hypernym of barrel cactus; that is, cactus is a word with a broader meaning than barrel cactus:

barrel cactus: any cactus of the genus Echinocactus; strongly ribbed and very spiny; southwestern United States to Brazil
cactus: any succulent plant of the family Cactaceae native chiefly to arid regions of the New World and usually having spines

barrel cactus (noun)	cactus (noun)
a cactus of the genus Ferocactus: unbranched barrel-shaped cactus having deep ribs with numerous spines and usually large funnel-shaped flowers followed by dry fruits	any succulent plant of the family Cactaceae native chiefly to arid regions of the New World and usually having spines
any cactus of the genus Echinocactus; strongly ribbed and very spiny; southwestern United States to Brazil