Psychic abilities are among those paranormal phenomena that have gained wide scientific recognition. They include abilities that involve perceiving information other than through the conventional senses (extrasensory perception or ESP), manipulating the physical world through the power of the mind alone (Psychokinesis) and reading and manipulating minds (Telepathy).
While there are many mutants with strong psychic abilities baseline humans can have them as well, though this is often thought to require a special talent, and origin heroes have them very frequently.
Psychic and psionic are used more or less interchangeably, and psi is often used as the noun corresponding to these adjectives, but confusingly is used as a shorthand for telepathy or telepath at other times.
ESP or esper and telepathy are frequently contrasted and otherwise treated like separate categories despite mind reading being technically extrasensory and despite the problems this causes in differentiating them, for instance the question to which one Empathy belongs. At other times telepathy is contrasted with clairvoyance, using the term as a super-category for ESP types.
Psychokinesis is sometimes contrasted with telekinesis, telekinesis being restricted to remotely moving objects, though sometimes telekinesis includes touch range. Occasionally Psychokinesis is contrasted with kinesis, which also includes cryokinesis, pyrokinesis and electrokinesis. At other times the term psychokinesis extends to those categories as well.
PSI is a general rating of psychic ability that is still used in some instances, especially for older mutants, but is mostly being phased out in favor of ratings in the specific PSI traits that a mutant manifests. It is mostly only used in cases where the mutant has a wide scope of psychic abilities. Since 'most' mutants only have a couple specific traits, they are rated with those specific traits instead of the broad category.
TP, Emp, and TK are the three most common of these specific traits (Telepathy - communicating through images or words mind to mind, Empathy - reading or broadcasting emotions from mind to mind, and Telekinesis - application of force on objects through will). The ratings of these traits tend to follow the more common testing standards where conceptual method is the primary logic behind rating... however, as with Psychokinesis (PK), Exemplar (EX), and most Energiser (EN) traits; this also tends to scale with power/control.
Most of the other abilities under the PSI umbrella are still generalized somewhat under the category of ESP. This is mainly because there simply aren't enough cases for a 'standard' rating for them to have developed. This is ironically, probably, one of the biggest cases of confusion for mutant manifestations actually. In truth, there are probably far more ESP type manifestations than any other trait... but these are also the abilities that can almost always be hidden unnoticed. And thus, the teen never attends Whateley or shows up in any situation where testing would be required. In general, ESP traits are rated based on reliability... with 3 being a fully under conscious control ability (also keep in mind that this is based on 'potential' not on current skill level... so even a Psychometric - 3 attending Whateley in his first year wouldn't have perfect control... but given training and time, he will).
PK - Psychokinesis - is actually a subconscious mental energy construct. For the most part, PK manifests as a skintight shell around the body and acts as a fully functional exoskeleton. It allows the body to resist or exert force based on mental power, not on the physical action of the body. Under some circumstances, many PKs are able to extend this surface along any object they touch in such a way as to provide structural support for that object as they move it... thus making it possible to lift a long object from its end despite the more likely occurrence that the object would bend or break under the strain. PK almost always works through physical contact... only very rare PK's can extend their shell away from the body without being in contact with it at some point.
A PK is not likely to be able to do things along the lines of what is seen in Star Wars by Jedi... Force Push, Throws, Force assisted jumps, etc are more likely the actions of TK.
Psi appears to behave like a physical substance in several ways.
Psychic abilities seem to require psi to pass through the space between the user and whatever is to be affected or examined. They can be warded against, and at least some wards function by preventing them from passing through a layer protecting a volume of space rather than negating them throughout the volume. At least forms of telepathic contact involve a psychic thread running between the brains of the two parties, and this thread can be made visible.
Psychokinesis sometimes offers tactile feedback and can take physical form, as a touchable and often visible object made of psi, or a psychokinetic shell around the user. In either case it shares many of the properties of manifested matter, including potentially causing MATD, as is the case with Mega-Girl.