elf vs faery

elf and faery both are nouns.

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

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

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

elf (noun)	faery (noun)
(folklore) fairies that are somewhat mischievous	the enchanted realm of fairies
	a small being, human in form, playful and having magical powers