red pepper vs cayenne

red pepper and cayenne both are nouns.

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

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

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

Other synonyms of red pepper include cayenne pepper.

red pepper (noun)	cayenne (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
very hot red peppers; usually long and thin; some very small	a long and often twisted hot red pepper
	plant bearing very hot and finely tapering long peppers; usually red