chili vs cayenne pepper

chili and cayenne pepper both are nouns.

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

As nouns, cayenne pepper is a hyponym of chili; that is, cayenne pepper is a word with a more specific, narrower meaning than chili:

Other hyponyms of chili include jalapeno, jalapeno pepper, cayenne.

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