The preternatural or praeternatural is that which appears outside or beside (Latin præter) the natural. In contrast to the supernatural, preternatural phenomena are presumed to have rational explanations that are unknown.
The term is often used to distinguish from the divine (supernatural) while maintaining a distinction from what is known and understood. For example, in fiction, vampires are often portrayed as having preternatural qualities and capacities that greatly exceed those of normal people, apart from unnatural powers that no creature could hope to possess.
Not that labels are the most significant thing but at times maybe this word would fit better for that which some intend? I know I often would have used this word in the past over Supernatural had I known of it.