The term Faerie is derived from "Fé erie.” It means the enchantment of the Fées, while Fé is derived from Fay, derived from Fatae, or the Fates. The term originally applied to supernatural women who directed the lives of men and attended births. Now it has come to mean any supernatural creature tied to the earth, except monsters and ghosts. The modern term, “fairy,” was created, due to fairy tales.
In Ireland, the Faeries are called the Aes Sídhe (the singular being Aes Sídh). Sídhe happens to be the name for the earthen mounds and hills dotting the Irish landscape. Irish tales claim the Faeries live under these mounds, so the term "sídhe" has come to mean Faerie in general. The word also refers to the palaces, courts, halls, and residences of the Faeries. Fairies are also known b y other euphemisms, "the Fair Folk", "the Good Neighbors", "the Little Folk", "the Little Darlings", and "the People of Peace". The reason why: first is to avoid attracting their attention. The second was to avoid insulting them.
Thanks to legends and folklore of Scandinavia the elf was used the same way Aes Sídh was used in Ireland, to refer to any Faeries, and it was introduced to Britain by the Anglo-Saxons. English literature made the elves the diminutive fairies of Spenser and Shakespeare, which in conventional Faerie lore would be the equivalent of the little nature spirits.
There are tales in myths of how fairies came to be. The first way had them as fallen angels. A few did not follow Lucifer into Hell, but decided to reside on earth.
Second: It is explained them as the dead not good enough to enter Heaven, but too good for Hell. It is said they live in limbo as they recreate their former lives.
Third and last: This has them as children of Eve. She hides them from God, who curses her that the children she tried to hide from Him would remain hidden from her, and subsequently all Mankind.