good-bye vs farewell

good-bye and farewell both are nouns.

Word	Noun	Adjective	Verb	Adverb
good-bye	Yes	No	No	No
farewell	Yes	No	No	No

As nouns, farewell is a hypernym of good-bye; that is, farewell is a word with a broader meaning than good-bye:

Other hypernyms of good-bye include word of farewell.

good-bye (noun)	farewell (noun)
a farewell remark	the act of departing politely
	an acknowledgment or expression of goodwill at parting