cayenne pepper vs red pepper

cayenne pepper and red pepper both are nouns.

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

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

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

Other synonyms of cayenne pepper include cayenne.

cayenne pepper (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