If you're looking for the card game, check Magic: The Gathering
Magic is a term that encompasses supernatural powers found in many games. These allow a person who learns how to use magic to create fantastic, supernatural effects. It could be evoking inherent mystical forces in the world, or invoking spirits to do thy bidding, flexing psionic brainmuscle, or wielding an item of unknowable power... but it all has this in common: you can't do this stuff in real life, but you can get away with it in the game. Usually only a vast minority of the population can perform supernatural magic, but some game settings (e.g. TSR's Dark Sun) make it common.
Magic is spelled magick if you are a homo or four hundred years old.
Most magic systems try to divide up all possible supernatural effects into categories. Four By Five Magic is probably the simplest example, damn near identical to Ars Magica but without copyright junk and easier to remember. Mage: The Ascension had all of reality divided neatly into nine categories before throwing it all away so they could sell more product with Mage: The Awakening.
Magic in D&D
D&D's Schools of Magic
- Abjuration - protection, prevention, barriers, wards, your "Protection From Evil" and "Dispel Magic" type spells.
- Conjuration - creating (temporary) things out of nothing, summoning far-away things to here. Summon a monster to fight for a minute, or teleport your target to here. Also covers personal teleportation, which is like summoning yourself to over there.
- Divination - see the invisible, know the unknowable (row row fight the powah). "Detect Evil" goes here.
- Enchantment - charm, dominate, antipathy, mind control stuff that clobbers free-will.
- Evocation - KABOOM! Like conjuration, but you're creating energy out of nowhere and venting it at a target. Fireballs, lightning bolts, and laser blasts.
- Illusion - make people see/hear/sense things that aren't there, or the exact opposite in the case of invisibility spells. Unlike Enchantment, you don't have to target a person, just the place or thing you want to look/smell/sound different.
- Necromancy - mucking with dead things, or life-force stuff. With the use of necromancy, dead girls can't say "no."
- Transmutation - change one thing into another thing. "Polymorph Other" goes here, along with those very very valuable buff spells for your meatshields.
For some reason, healing spells in D&D are considered "conjuration" spells, not "transmutation," despite changing a broken bone into a not-broken bone, and it's not "necromancy" despite mucking with life-force stuff. In older versions of D&D, healing was considered Necromancy, so, whatever. This has changed in 5th edition, in which "insta-heal" spells like Cure Wounds and Healing Word are considered Evocation, spells like Regenerate and Goodberry are part of the Transmutation school, Restoration and similar are Abjurations, and the Raise Dead type spells are Necromancies. Basically, the healing-related spells are assigned a school as appropriate, rather than lumping all of them into a singe school of magic.
Magic in D&D 3.5e
Magic in Dungeons and Dragons 3.5e is called the art by elves and other such nonsense by other such nonsensical creatures. It is similar to the weeaboo idea of chi/ki where magic is all around us like the force from Star Wars, like the holy Gandalf in religion and the.... yeah you get the picture. Magic in 3.5e is everywhere like pedobear.
To cast spells you first need to know the spell (if it is an arcane spell) which makes sense - you can't differentiate an integral if you don't haz mathz. Divine spell casters have it easy though, their god/deity/imaginary friend lets them cast any spell if they have enough levels and if they ask really nicely in the morning.
Casting the spell takes "a lot" of effort (seriously, magic users in D&D are physically weak) so they can only cast a certain number of spells from a certain casting difficulty per day. Except for Warlocks and Dragonfire Adepts, who cheat by not actually being wizards themselves and begging for power from something else without even putting in the personal effort a Cleric does to prepare spells. They just kinda channel someone else's power and use supernatural abilities that look a lot like spells but somehow technically aren't. This became more and more of a thing as splatbooks increased, with new magic systems being released that operated by different
awesome and cool terrible and weird rules.
- Psionics, a very old system that was even included in the SRD, is pretty much reflavored spellcasting, except with a mana reserve referred to as power points and the potential to become massively overpowered.
- Binding, a thing that Binders do to temporarily graft weird spirit-bits to themselves to get at-will abilities and bonuses that technically aren't spells but that do allow monster summoning, Wall of Stone, and the ability to rebuke undead.
- Shadowcasters had a thing. It was terrible, and basically involved using their own magic system to pretend to be inferior versions of an illusionist.
- Truenamers existed, but they were so incredibly terrible and badly written that no-one ever played them and they never got any support - not even web enhancement stuff like Binders and Incarnum users got! They could say magic words and do magic that wasn't actually involve spellcasting, but was instead at-will and based on skill checks with weirdly scaling DCs.
- Incarnum, a very confusing system that was released during Dread Cthulhu's brief employment at WoTC
- The Book of Weeaboo Fightan Magic, which refuses to call itself magic but still allows teleportation, fireballs and the ability to stop time. But you're holding a katana so it can't be pussy Vancian magic, right?
Magic in D&D 4e
In 4E, familiar spells from prior editions still exist, though many of them have disappeared, and many spells that have the same names as in 3.5 function in a much weaker manner, such as fireballs that cannot kill even a low level monster, or 'disintegrates' that do little more damage than a skin rash, 'teleports' that barely cover the distance of a room. All in all, the spell selection is significantly smaller in 4E, with many spells removed, particularly ones that would require effort of a human GM to adjudicate. Indeed, in 4E, spells are less intricate and specific, and more straight-forward.
Another notable point in 4E magic is the fact that classes don't generally share spell lists anymore, and that all classes are comprised of abilities that are basically spells. For example, the Wizard and Sorcerer have wholly different selections of spells and class features, and generally have a list of spells only moderately different in effect than the fighter's spells, or the rogue's. Spells in 4E are classified with powers, meaning a spellcaster is going to generally have about as many spells as a Fighter has special attacks, stances, and disciplines. They're also functionally similar, differing only in affect, but not in the usage of attack rolls to resolve the success of the spell. This has led to the prevalent criticism that "all classes in 4E are spellcasters."
There are also rituals, which are questionable magic effects that take a while to occur, and cost sometimes far more money than a reasonable player would be willing to spend (such as a fairly expensive ritual that would allow you to listen behind a door 20' away). They generally have out of-combat purposes, unlike most of the typical spells like those mentioned above, which are almost exclusively for combat.
Magic in D&D 5e
5th edition's magic is similar to what was seen in 2e and 3.5, with some notable differences. First, spells whose only difference were power level were consolidated into single spells. So instead of "Cure Light Wounds," "Cure Moderate Wounds," etc., there is a single "Cure Wounds" spell, which is more effective when cast using a higher level spell slot. By a similar token, the Bigsby's _____ing Hand line of spells and similar were reimagined as a single spell, whose effect is determined on every casting. There are still technically Arcane and Divine classes of spellcasters, but the difference between Arcane and Divine magic is largely fluff-based, with little mechanical effect.
Perhaps the most significant change is the return of Vancian Spellcasting, albeit in an altered form. Spellcasters in 5th edition are broadly divided into a pair of categories: prepared casters, or spontaneous casters. The former chooses spells from a greater list that it can cast each day, and the latter has a smaller repertoire of spells known, which it can always cast. In earlier systems, a character would have a certain number of spell slots, and prepare spells by assigning one for each slot (If you wanted to cast Fireball three times that day and Magic Missile twice, you would need to prepare three copies of Fireball and two copies of Magic Missile). 5th edition prepared casters only have to prepare spells that they wish to cast that day once, and may cast them as long as they have spell slots (A character with three 1st-level slots that had Burning Hands and Sleep prepared could cast Sleep twice and Burning Hands once, Burning Hands three times, or any other combination).
Magic in Warhammer
Warhammer 40k's Schools of Magic
Oh wait, there are actually five psychic schools in 40k - they all originated from Dark Heresy books, but became known to wargamers through the 6th edition 40k rulebook. Fluff wise they were founded by the Thousand Sons and Magnus the Red. Also, pretty much everything the Imperium knows about psychic powers and sorcery is taken from remnants of the Tizca libraries on Prospero.
- Biomancy - Manipulation of flesh - your own, your ally's, or your enemy's. This includes healing and buffs (some self buffs can turn psykers into death machines that eat up dedicated combat HQs), as well as abilities that cause people to vomit to death or literally explode. For some reason biomancers can also shoot lightning, which is explained by using their nervous system to generate unholy levels of high voltage.
- Pyromancy - Killing things with fire. Fireballs, flamethrowers, fiery swords or melta beams are their specialty.
- Telekinesis - Moving things with the mind. Known to create tough kine-shields and barriers to protect allies, as well as smashing things with other things (think human sized lifta-droppa) or for extra lulz using more subtle things with less powerful but highly accurate telekinesis - like jamming guns or pulling out the pin from a grenade on the enemy's belt.
- Divination - Foreseeing the future and messing with probability. Can be a real pain in the ass, guiding a few strong units with knowledge of the ways of the future. Known to be the most nerdy of all psykers, divinators almost always possess more knowledge than other psykers about how their powers work, and about how the Warp works in general.
- Telepathy - Reading and manipulating minds. Illusions and mind control are their powers, as wall as causing fear and panic or making heads explode.
Magic The Warp in Dark Heresy
Unlike in most D&D, where everything's colourful and cheery, trying to use ethereal powers in the 40,000 universe could get your "beautiful snowflake" soul stolen by nasty daemons who will then rape the shit out of your body and then defecate on your eyeballs.
On the plus side, Psykers (as magic users are called) know very few powers (two at the start) in the game but can cast them whenever they want as long as they don't fail the casting roll. Failing the casting roll can cause hilarious effects, if you're the kind of person that laughs at safety videos for farm equipment.
In Warhammer Fantasy, magic plays a huge part in both the fluff and on the table top. Magic is used to keep whole armies standing up, to write shit on rocks fired by Dwarven artillery pieces, and everything in between. The eight Winds of Magic which emanate from the Realm of Chaos are harnessed by most wizards around the Warhammer world, but some wizards like the Chaos Sorcerers of the Northern Wastes use magic in its rawest form. The eight Winds (one for each point on the star of Chaos) each have their own Lore practiced by their Imperial College of Magic, but most races also use their own form of magic along with or instead of some or all of these Lores. The eight Lores and their respective Winds are as follows:
- Fire: Like Pyromancy in 40k, this Lore revolves around burning things. Naturally, this lore has lots of magic missiles and direct damage spells, with the odd hex or augment thrown in for variety. The signature spell (like a 40k Primaris Power), Fireball, is very useful, reasonably powerful, and easy to cast. Most armies have access to the Lore of Fire, which is generated by the Wind Aqshy. Imperial wizards that use this Lore are known as Bright Wizards.
- Heavens: The Lore of Heavens is used to scry the stars for future portents. This sounds unusual, but it can be a very useful lore to use. Its spells include unleashing lightning on poor souls, divining the future, and even sending a motherfucking COMET falling onto the enemy. This Lore is created by the Wind Azyr and is practiced by the Celestial Wizards.
- Light: Light works excellently against Daemons, Undead, or armies with high I/WS, but falls to bits against anything else (OG and Dwarf players just laugh a lot). Other than Banishment and Shem's Burning Gaze, most of the spells boost your army's WS or I stats to rape-tastic levels. The Wind Hysh makes this happen, and it is studied by the Light Order of wizards.
- Life: This is basically Biomancy (along with the Lore of Beasts), and boy, can it work miracles. Not many armies can take this, only the ones that can stand its supreme amazingness. It makes your men abnormally tough, eats your opponent with the ground and can even BRING YOUR MEN BACK FROM THE MOTHERFUCKING DEAD! Is it awesome? Yes, Mr. Skittles Guy, it is awesome! The Jade Wizards that use it tap into it from the Ghyran Wind.
- Death: Kills shit. Amethyst Wizards wield the wind of Shyish to pretty much end anything. They're almost like time mages than necromancers, using Shyish to fast-foward the life of an enemy until they turn to dust. They have a strict policy against undead and necromancy. They're mostly used to combat the undead. Ironically everyone accuses them of being necromancers because they look spoopy.
- Shadow: An illusionist school by another name, while focusing on the darker aspects. Grey Wizards (not Gandalf) use the Wind of Ulgu to make people forget you were even there, mess with minds, and turn invisible. Mostly employed as spies and assassins.
- Metal:Gold is a great conductor of magic and the Alchemists of the Gold order use their powers taken from the Chamon Wind to turn people into solid gold, attack people with metal death dogs and enhance or weaken weapons and armor. They're also reputed to be the wealthiest of wizards due to turning lead into gold, but they deny this.
- Beasts: The Lore of Beasts makes up the other half of Biomancy, with the scarifying of the user and their allies to improve their bodies. This lore is used by
Radagastthe Amber Brotherhood and involves mutating more limbs to RIP AND TEAR, attacking people with crows and turning yourself into a fucking DRAGON! Trust me, this lore IS THE SHIT.