cayenne pepper vs capsicum

cayenne pepper and capsicum both are nouns.

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

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

cayenne pepper: plant bearing very hot and finely tapering long peppers; usually red
capsicum: any of various tropical plants of the genus Capsicum bearing peppers

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

cayenne pepper (noun)	capsicum (noun)
ground pods and seeds of pungent red peppers of the genus Capsicum	any of various tropical plants of the genus Capsicum bearing peppers
a long and often twisted hot red pepper
plant bearing very hot and finely tapering long peppers; usually red