Now I'm just confused. I'm thinking "Fey" have to be 1) Humanoidish, and 2) possess innate magical ability ........I mean, at birth.
I don't think either is necessarily required. I think you could reasonably have fey that were not particularly humanoid in form and did not possess any notable innate spell ability.
In general, D&D never really defined 'fey' or 'fairy'. The notion began to take shape when 3e began to distinctly classify monsters as 'animal', 'beast', 'dragon', 'aberration', etc. However, to my knowledge, 3e didn't attempt to provide any coherent single mythic basis for each of these categories, leaving that up to the individual DM. Fey in my campaign therefore retained their homebrew origin as the 'small gods' of the fern and flower that predated the later gods that were born from the fruit of Yggdrasil (a conception that was independently created in parallel with that presented in 'The Book of the Righteous', probably with similar real world mythic inspiration). Fey also provided the basic design template that the gods would later use to create the humanoids (so in fact, humanoids are vaguely feyish in my campaign world rather than fey being vaguely humanoidish). Fey in my campaign world are basically close kindred to the elementals, and could be considered a sort of prime material elemental. The close semblance between the fey and the elementals can be seen in elementals such as the sylph and nymphs, that share with fey both demeanor and natural form. Fey are just prime material stuff that gained life and sentience at the same time the animals and plants were springing up, apparently through some basic chaotic principle of the universe (as in contrast to plants and animals, fey are overwhelmingly chaotic in nature). Some of them later migrated into other areas of the multiverse, particularly the far ethereal (now often called Fairie) and the near astral (the so called Dreamlands) and later the dominions of certain chaotic deities whose outlook they shared, but fundamentally they are simply the eldest and oldest incarnations of the material world. Among the fey, there is a belief that the eldest of the fey on first awakening saw the Nameless Creator's back as he departed from the multiverse.
So that is who the fey were and are for me, but when 4e came along they decided to give all of 3e's categories a definitive mythic explanation. So, as pemerton pointed out, in 4e fey simply refers to denizens of the feywilde. That is to say, "Fey are from fairy." To me this rather reverses the story of my campaign world (and incidently, of the real myths of Earth as well), in that rather than having fey flee to fairy as they are pushed out by people gradually causing this world to fade somewhat, it has them invaders from some other world. Ultimately, there is nothing wrong with that and the 4e world is interesting in its own right, but it always struck me that 4e's various canonical inventions were no more than some DM's homebrew being allowed to take canonical status. This is particularly true of the areas where 4e departed canonically from what had been canonical myth and origin stories in prior editions.
All of this is just a long preamble for getting around to saying that ultimately, fey are simply whatever you decide is best for you own campaign. By and large this isn't a settled question with a single canonical answer. At best you could say, "What are fey in X edition?" or "What are fey in X campaign setting?" There is no universally accepted definition of fairy.
