elf vs fairy

elf and fairy both are nouns.

Word	Noun	Adjective	Verb	Adverb
elf	Yes	No	No	No
fairy	Yes	No	No	No

As nouns, fairy is a hypernym of elf; that is, fairy is a word with a broader meaning than elf:

Other hypernyms of elf include faerie, faery, fay, sprite.

elf (noun)	fairy (noun)
(folklore) fairies that are somewhat mischievous	a small being, human in form, playful and having magical powers
	offensive term for a homosexual man