3 somewhat different levels: 1. An enhanced, superior ability of some type; but not supernatural, linked in some way to "Spiritual" techniques. The shortcoming of this set is that such abilities can be gained by those not practicing any Spiritual Sadhana, so there's a difficulity associating the Siddhis to the Sadhana, as to cause and effect.
Examples: Certain disciples of Sri Chinmoy have in the past broken various athletic records, claiming an association to their meditation techniques and Chinmoy. Chinmoy himself bragged about dead-lifting weights, putting himself into some type of "extraordinary" category; but further investigation into his exploits turned up nothing of the kind. ... In short, enhanced abilities in this category can't be proven to be caused by Spiritual techniques. Anybody can butt-bounce. 2. Very extraordinary abilities that can't easily be explained, but short of supernatural. Example: the mathematical discoveries of Ramanujan, definitely astounding and inexplicable by ordinary standards. He seemed to be able to pluck formulas out of thin air (but not all of the formulas have panned out as being true). He first attributed his abilities to a certain Divine Mother Goddess; but after living in England, disavowed any assoication with the Deity (and continuing to make remarkable discoveries)...; so go figure. 3. Abilities clearly in the supernatural category, such as manifesting trinkets our Vibhuti out of thin air; amazing but improbable mental feats, true levitation, invisibility, etc. Manifesting Vibhuti out of thin air seems to be a well known phenomenon in India. I've seen it myself and would swear that no tricks were involved. '