Actually, fairies are one of the nigh-universal things in cultures globally. In Japan, you have the fox people and the tengu. Amongst the Hurons, you have the little turtle people. Algonkian cultures also tend to have fairies. They turn up in Lapp mythology, and, more memorably and recognizeably, European and Middle Eastern myths. The Djinn, though, I would argue are not nearly as closely analogous to fairies than the Peris are. Indeed, the modern fairy seems to be essentially a hybrid of the Celtic and Persian fairy myths seen through the lens of Germanic culture.