The Elementals are the spirits that manifest themselves as one of the four elements: Fire, Water, Earth and Wind. The Slyphs are an elemental that have yet to appear in the series. (However, they have been mentioned in weapon history of Apostate's Misery.)
The spirits of fire and water, Salamander and Undine, the spirits of wind, Sylph, and the spirits of earth, Gnome, are known as the four great spirits. Each of them is without a distinct form, an existence something like a sprites. Moreover, aside from this spirit group of monsters exists the avatar of flame, Ifrit, and evil spirits called Ghosts, Wraiths, Spirits and the like.