A fairy (also faery, faerie, fay, fae; euphemistically wee folk, good folk, people of peace, fair folk, etc.) is a type of mythical being or legendary creature, a form of spirit, often described as metaphysical, supernatural, or preternatural.
Pixies (also Pixy, Pixi, Pizkie, Piskies and Pigsies as they are sometimes known in Cornwall, England) are mythical creatures of folklore, considered to be particularly concentrated in the high moorland areas around Devon and Cornwall, suggesting some Celtic origin for the belief and name - akin to the Irish sidhe believed to inhabit ancient underground ancestor sites such as stone circles, barrows, quoits or standing stones.
A Gnome is a diminutive spirit in Renaissance magic and alchemy, first introduced by Paracelsus and later adopted by more recent authors including those of modern fantasy literature. Its characteristics have been reinterpreted to suit the needs of various story-tellers, but it is typically said to be a small, humanoid creature that lives underground.
An elf (plural: elves) is a type of supernatural being in Germanic mythology and folklore. Elves are first attested in Old English and Old Norse texts and are prominent in traditional British and Scandinavian folklore.