cayenne vs red pepper

cayenne and red pepper both are nouns.

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

As nouns, cayenne and red pepper are synonyms defined as:

cayenne and red pepper: ground pods and seeds of pungent red peppers of the genus Capsicum

Other synonyms of cayenne include cayenne pepper.

cayenne (noun)	red pepper (noun)
ground pods and seeds of pungent red peppers of the genus Capsicum	ground pods and seeds of pungent red peppers of the genus Capsicum
a long and often twisted hot red pepper	very hot red peppers; usually long and thin; some very small
plant bearing very hot and finely tapering long peppers; usually red