I gleaned this fascinating information in a Google search:

The word fay came to English around 1400 (as fai, fay) from Old French faie or fee (Modern French fée), earlier from the Vulgar Latin feminine fata, referring to one of the Fates, personifications of destiny (the Greek Moirae); cf. the Italian Fata Morgana used as a translation of Morgan le Fay.

English fairy (Middle English faierie) was borrowed ca. 1300 from Old French faerie "land of the faie, enchantment", a noun denoting the general class, activity or habitation of the faie (faierie being related to fai as e.g. yeomanry to yeoman, foolery to fool, or nunnery to nun).

From adjectival use ("fairy gold", "fairy queen" etc.) from the 15th century applied to the class of supernatural beings inhabiting faerie, re-interpreted as derived from fair, singular fairy with a new plural fairies.

The term fairy tale is a translation of the Conte de feés of Madame d'Aulnoy (1698).

The spelling faerie first appears 1590 in Spenser's Faerie Queene.[81] From Spenser's use, the spelling with -ae- came to be used in a dignified or poetic sense as opposed to "vulgar" tales.

J. R. R. Tolkien makes use of the distinction, in On Fairy-Stories defining Faërie as "the realm or state in which fairies have their being", depicted (under the name of Faery) as a mystical or visionary state in his Smith of Wootton Major.

 Fairy Land is used by Shakespeare as an apposition, in the 19th century contracted to fairyland.