cone pepper vs capsicum

cone pepper and capsicum both are nouns.

Word	Noun	Adjective	Verb	Adverb
cone pepper	Yes	No	No	No
capsicum	Yes	No	No	No

As nouns, capsicum is a hypernym of cone pepper; that is, capsicum is a word with a broader meaning than cone pepper:

cone pepper: plant bearing erect pungent conical red or yellow or purple fruits; sometimes grown as an ornamental
capsicum: any of various tropical plants of the genus Capsicum bearing peppers

Other hypernyms of cone pepper include capsicum pepper plant, pepper.

cone pepper (noun)	capsicum (noun)
plant bearing erect pungent conical red or yellow or purple fruits; sometimes grown as an ornamental	any of various tropical plants of the genus Capsicum bearing peppers