Yes. “Fey” is the correct spelling. They use it because while they are fae, and also fay, they are in fact fey, so they are constantly starving to death.
Their world name is the Silver DawningThe parallel world of the Fey. It’s colorful. More. It’s colorful, to say the least, and highly changeable; they tend to switch it around however they feel, so maps aren’t terribly reliable in that place.
Like all magical beings among the MythosThe Mythos refers to six of the Seven Peoples of the Earth, i.e. the Sun and the Darkness, the Guardians... More, they are naturally magical, producing their own power like an electric eel generates shock – but unlike every other member of the Mythos, their magic is being stolen. The ThroneSee Mab (throne) and Jaden (scepter). More and the Scepter siphon their power from birth, leaving any Fey claimed by those two artefacts of power starving.
The Fey have found ways around it. They can weave magic from human love and other emotions, as well as other people’s magical arcanum. However, it isn’t easy, and makes it nearly impossible to live away from their home world. At least while they live at home, the Throne and the Scepter both eke enough magic back out to keep them alive.
The primary groups among the Fey are the Seelie and Unseelie, who resemble humans, though they have long, pointed ears. Males are called feyor. Females are called feyan.
As Fey age, they their skin and flesh lose their softness. In the end, when Fey are about to die (if they survived to old age, that is), they resemble statues.
Trivia: DragonsSome of the most dangerous beings among the Mythos, and not just because of physical size and strength. More call them children of the grasses because they scuttle around in the grass (from a dragon’s point of view).