Fey is traditionally an adjective meaning (1) fated to die or (2) in a disordered state of mind like one prepared to die, while fay is traditionally a poetic noun referring to a fairy or an elf (fay has the same Old French origin as fairy). Today, the two words have melded into the sense of fey most English speakers are familiar with—fairylike, elfin, or otherworldly. The darker definitions of fey are mostly gone, and the original fay is now just an archaic variant of fairy.
There are still some who insist the newer sense of fey is wrong—and a few dictionaries still list only the old definitions—but the change is well established in general usage.
Here are a few historical examples of the two words in action:
Like fays, like fays, / Like merry tripping fays, like fays, / We tread the maze, / Like fays we tread the maze / On midsummer’s green, / And where we have been / The prints of our dance in morn shall be seen. [The Universal Songster (1810)]
And Grier thought he wore upon his face the fey look of those who hold a resolved course to death. [Macmillan's Magazine (1897)]
This was a fay so transmuted, who, grateful for her deliverance, offered to enchant the horse and arms of Brandimart. [1823 translation of The Orlando Innamorato]
“Still, Eric, of a sudden I grow fey : for it comes upon me that I shall not die to-night, but that, nevertheless, I shall die with thy arms about me.” [Eric Brighteyes, Henry Rider Haggard (1884)]
And these recent examples show how fey is now typically used (fay is now very rare):
I’ve lost interest in Sookie’s world since it became overrun with faeries and other fey beings. [io9]
But he’s taken this most masculine of identities and remade it as a fey, wimpy, cardigan-wearing, gladiola-loving singer. [Ask a Mexican, Gustavo Arellano]
Their fey ways, affluent lifestyles and insistence on capturing on canvas the everyday lives of villagers were about as alien to the residents of Street-an-Nowan or Tolcarne as a pilchard jumping out of its net and singing the National Anthem. [This is Cornwall]
[A]nd youthful Malcolm, the future king of Scotland, has been transformed into a fey surfer boy with a penchant for showering with his soldiers. [TheaterMania]
Japan’s debut is a groundbreaker, a fey fusion of funk-
inspired rhythms, space-age synths, and guitars locked totally in a Stygian glamrock. [Alternative Rock, Dave Thompson]