One thing I noticed, and most of you also did I assume, is that all sprites are bound to a crystal core. That said, Sprites are probably surges of elemental energy concentrated in/around crystallized aether, corrupted most of the time. I believe that sprites are only elemental manifestations of accidental surge magic, which is directly related to what kind of element is worshiped in said place and the environment itself. That'd explain why there is no ice sprites in any other place other than Coerthas, or why water sprites are scarce around Eorzea and concentrated mostly around wet zones like La Noscea and The Black Shroud.

Also, you can notice similarities among similar sprites, like Fire and Lightning, both their forms being made of a glass-like structure that relates to their high temperature.