cayenne pepper vs chili pepper

cayenne pepper and chili pepper both are nouns.

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

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

Other hypernyms of cayenne pepper include chile, chili, chilli, chilly.

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

cayenne pepper and chili pepper: plant bearing very hot and finely tapering long peppers; usually red

Other synonyms of cayenne pepper include Capsicum annuum longum, cayenne, chilli pepper, jalapeno, long pepper.

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