Magic
While magic is the most ubiquitous esoteric power on Earth, it is nearly unheard of in the larger universe, though it is relatively common in a handful of realities with similar histories (which makes them close neighbours to the main universe, metaphysically-speaking).
This is caused by the unique nature of the pre-Shattering world. The effect caused by perceiving and being perceived resulted in what humans generally agreed to be supernatural beings not being able to interact with normal humans, unless expected. Mundanes (also known as baselines or baseliners, short for baseline humans) and supernaturals essentially lived in different worlds until the Fall of Berlin. In areas with many human observers, a were, for example, could not touch anything or enter any building, even if the humans happened to be looking in their directions. From the were's perspective, it looked like they were caught in a literal ghost town, where they could not interact with anything.
The reptilians, who did interact with small numbers of humans throughout history (though, between the mindwipes necessary to survive the aftermath of the events the Collective arrived to stop, and the rattled state of the survivors who did not want to live in a world where the Zhayvin were needed, the memories and records never stuck, except as fringe beliefs, such as the "Conquerors from Hollow Earth" conspiracy theories) concluded that aliens and other entities with paranormal powers were exempt from this effect. Besides their hypothesis that humans unknowingly, passively manipulated quantum states to an unusual level, quite literally making things unable to fully exist unless they believed in them, some reptilians mused that the human collective unconscious seemed to, somehow, be able to differentiate between, for example, a Ser Gris using psychic telekinesis, and a mage shapeshifting into one and using telekinesis based on mana, even if the observer themselves did not know the difference, or believed they were the same.
In the light of recent macrocosmic experiments, the Collective hypothesises that this was an artifical state, induced by the First Principle or its agents with the purpose of directing evolution so that it would result in the most diversity. This anthropocentric quantum separation effect, as the reptilians termed it, did not only extend to Earth, but the entirely of creation. With the aid of human volunteers, the reptilians concluded that humans could perceive and interact with alien paranormals, but not Earth-based ones, an arbitrary distinction that suggested meddling.
"Magic" is an umbrella term referring to activities requiring mana, ranging from casting and summoning to sympathetic magic, alchemy, enchantment, ward-making, artifice (a catch-all term for the creation of constructs and the shaping of materials without warding or enchanting them), divination and scrying. Casting, like artifice, is shorthand for using mana, but generally understood, in magic slang, to cover things like throwing fireballs or creating time lops, rather than remotely attacking people using their belongings as a focus, even though all spells and magical effects are "cast".
Mana is a metaphysical energy created by the synergy of the body (not necessarily a biological or organic one, inorganic shells or avatars count as equivalents), mind/processor and soul. While humans need a balance between the three components of their self (and their subdivisions, depending on a particular mage's beliefs), and the weakening or absence of one can cause them to become incapable of casting, there are incorporeal, mindless or soulless beings able to cast: ghosts, specialised golems, demons and angels (though it would be more accurate to say they are a more primal form of soul, rather than soulless, like wood is for paper), to start. Though a strong mind is conducive to magic, the mind must be strong in the metaphorical sense, rather than the amount of brain cells, brain activity or processing power, as concluded by the reptilians' attempts to study mana. A sapient supercomputer would not necessarily be a stronger mage than a human of average intelligence if all it can do is crunch numbers.
To most arcane senses, mana appears light, shining blue, with light green highlights or "veins". Though it can manipulate or be converted into natural forces, mana phases through them in its raw state, and even if solidified into mana objects, it appears as anomalous, with no detectable density or mass, although a building-sized "block" of mana created by the average mage will act although it is as durable and heavy as a building. Solidified mana can be burned or dissolved, though not frozen by mundane temperatures, and floats under its own power, though it can be torn apart or crushed by sufficient levels of gravity, causing it to dissapear.
Each mage has a mana pool, appearing as an outline around their metaphysical self, though many envision it as an actual pool, lake or well, located in the centre of their being. A mana pool is inexhaustible: a mage can cast as many times as they like without running out. The limits are physical needs, which can be circumvented or removed with enough skill, and the "size" of a mage's mana pool. Most mages can manipulate the equivalent of a handful to a dozen tons of TNT at a time, and, in terms of more esoteric effects, can manipulate spacetime or gravity across an apartment building, even though the energies involved in such events might be far lower or stupendously larger than a mage's firepower limits, if they were to be replicated by mundane mundane technology. This is generally agreed to be a quirk of magic, which, if not sentient, is instinctively stubborn about following its own rules.
Mages can enhance their strength, durability and reactions by tapping into their mana, as well as removing the need for nourishment, rest or air. Sufficient exposure to inner or foreign mana will permanently enhance a mage's body while removing their physical needs, an effect that, unlike a ward or enchantment cast on the mage's body, can't be removed by antimagic, as they were altered by magic in the past.
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One in a hundred humans is a mage, their mana awakening most often after emotional events during childhood or adolescence, with born mages being rarer. Intense events can increase the size of a mage's mana pool, should they survive with their bodies and faculties intact.
Often, aside from baseline magical powers (control of matter, energy and spacetime, the creation of localised laws of physics and metaphysics, existence erasure), mages will have "themed" magic, influenced by their personality. Brazillion of the Circle Bizarre was passionate about mathematics before he obtained the power to divide, multiply and raise attributes at a whim.
Appropriate objects, collectively referred to as foci (although the term started as a classification for focusing tools such as wands and stave - things with the proper shape for channeling mana and pointing it at a target. Slingshots, bows and arrows and firearms have a similar effect), can help ease casting. Water magic is easier while holding a hose, even if the mage is not channeling mana through it; thinking about it is enough.
Spells are phrases and/or rituals that can trigger specific magical events, usually beyond the mage's innate capabilities due to either the necessary output or the nature of the caster's goal. They are the verbal, nonverbal and ritualistic equivalents to physical foci, and work through the same principle of focusing and strengthening the mana by helping the mage concentrate.
Wards are physical (in the sense they have a physical presence) or metaphysical shields, seals, cages or traps.
Although popular culture sometimes depicts magic and technology as opposite "forces" or sides, magic could be considered a type of technology: it is, after all, a practical application of knowledge, often using objects, or even devices traditionally considered "technological".
Antimagic
If counterspells are like diverting or damming rivers, antimagic is like vapourising them and scattering the steam. To a mage's arcane senses, antimagic registers as an unsettling force or absence, causing a feeling of unease, like balancing on the edge of a cliff. Most mages believe this is an instinctive reaction to something opposed to a major facet of their self, even if they do not know what antimagic is, exactly.
Antimagic is created during the extremely traumatic death of a mage, which, to use a visual metaphor, turns their mana pool into a pit or vacuum. This antimana covers an area equivalent to that the mage could manipulate in life, and shuts down all magical effects in said area: nothing can be cast, enchantments and wards disappear, and so on.
Antimana is to mana what the void that animates a vampire is to a soul; antimagic is a term used to refer to objects or beings imbued with antimana.
Psychic powers (psi, ESP, etc.) and counters (psilencers)
There have been few psychics in human history, and never many at a time. With the newest generation being born, psychics are appearing in numbers similar to mages, both among children born with psi and older people who manifest psi.
A psychic's mind, much like a mage's, must be strong, in the metaphysical sense, for their powers to work. Also like mages, their psychic grasp has a limit of power and reach, as well as, sometimes, an unique ability shaped by the psychic's experiences.
Psi is the term used to refer to psychic abilities in general, the most common ones being tele/psychokinesis, pyrokinesis, electrokinesis, and ESP. ESP, short for extrasensory perception, covers enhanced intuition, telepathy, empathy (which allows psychics to literally feel emotions), precognition, post/retrocognition, psychometry and remote-viewing.
ESP powers often overlap - a "bad feeling" can be caused by either enhanced intuition or immature precog, or even both working in concert. Psychometry is to touch what postcog is to imagination and the other mundane senses, allowing the psychic to learn about a being or object's past, or, in rarer cases, its present in more detail than their other senses allow. Remote viewing can be considered a form of long-distance enhanced intuition, accurately perceiving events far away despite sensory barriers.
Psilencers are methods and devices used to counter psi like antimagic is used to counter magic. A psychic's violently traumatic death has similar effects to a mage's, creating a psilent zone and giving some credence to the theory that the two forms of power are related, perhaps in the way strigoi and ghouls, undead who feed on lifeforce and flesh, respectively, are.
Among alien species, psychics are and have been common for billions of years, and there are multiple naturally psilent species, although the existence of antimagic beings is still being debated.
Faithcraft and demonology
Faithcraft is the act of tapping into the power of the deity one worships. Divine power is neither magical nor psychic, and can be differentiated from them by the permanent damage it deals to vampires, ghouls and strigoi. Faithcraft can be accomplished through prayer or by obtaining blessings, which are to divine power what enchantmnts are to magic.
Demonology refers to the theory and practice of tapping into the power of demons, either through contracts, binding them, or, more rarely, willing offers. Demonic energy, much like its holy counterpart, is neither magical nor psychic. Demonology can be practised through either megic or the power of the demon themselves.
Others
The nature of the Unmoved Mover's creation and the reminiscence most of its inhabitants bear to its five-pointed shape means there are many strange powers in creation that do not resemble any of the above: eldritch effects that break minds and existence alike, animal-based abilities such as those of therianthropes, vampiric powers, the manipulation of Archetypes, the very ideas that form the bedrock of creation, or even abilities that revolve around a being's perception by themselves and their peers, but which, unlike those of weres, are mostly unique, such as those of FREAKSHOW's Breakout.