1. Outward casting: moving magic immediately out for an immediate effect, whether wandless or using a wand or other focus to cast any charm, jinx, hex, curse, or counter curse. The pros are that the effect is immediate, and this is the most stable way to cast magic. The cons are that whatever you cast is temporary, and there is usually a way to reverse it. Whether a counter curse or just waiting it out.
2. Rune casting: Rune casting uses magical language, symbols, and imagery through rune script to hold magical energy, whether that energy is the magical energy of the user or of the ambient mana of a leyline or place of magical power. Much like fuinjutsu and coding, it saves a spell/command and then executes it with the stored energy. The pros are that you can execute spells you would have never been able to do by outward casting you can save up the magic energy, and achieve effects that you could never do on your own. The con is the time that is consumed learning runes, learning how to match up runic languages to get the effects that you want, and even then, the best runic formation can fail. However, most magical tools are made with runes. The standard runic tool works when the user's magic is supplying it, but runic tools made with alchemy, potions, and/or rituals can have effects that last a lot longer or continually store magic having effects that will last a lot longer especially if the items are tied to family magic
3. Mind's eye casting: Divination, scrying, Occulmency, Legimancy, the very apex of this branch of magic, the pensive. Astronomy is used to awaken the mind's eye.
4. Magic synchrony: Potions and Alchemy, and even herbology and magical creature rearing. In some ways, this isn't a way to cast magic by itself it goes hand in hand with both outward casting and runes, magic synchrony is like a short range ritual you send out your magic a continued flow of your magic unlike outward casting sending out an overwheling wave of power for a single spell, or runes storing magic for a delayed affect you consistently flow your magic in a set way to achieve an effect.
So, for potions, you consistently flow magic into the cauldron while you cook, which is its most stable form. The reason for this is that when cooking a potion, the potion acts like food; the smell of the potion makes you feel the specific emotion that you are trying to invoke, and that helps you focus to complete the potion. But the reason most people can't become amazing potioneers is that not every smell invokes the same emotion; either not enough of something to many turns on fire, or off the fire will give a different effect, and learning the ones that work for you is something that experimentation is required. Making it more of an art than an exact science. It is used in magical animal breeding and in herbology you sychronise your mana to another's magical signature in plants it promotes magical growth in animals it bonds you leading to a familar bond.
Alchemy is so uncommon because, by its nature, it is unpredictable as to create alchemic results you use magic synchrony and rune magic to consistently flow magic into runes to craft items that last longer and have stronger effects than standard runic formations.
5. Rituals: There are Four way to do rituals, There is nature based which is kind of like a druid ritual yearly say a few words pray to a few gods for power maybe you get lucky and you get a boost in magic controlling plants, or maybe even a boost in looks or longevity what they ask for is consistency and it doesn't work unless they like you, Demonic rituals you make a deal with a demonic entity for some of your magic money your soul they will deal with anybody and its always a losing deal, dimensional entity rituals which is what the entire Sorcerer faction is based off of, lastly are mana ritual that is where you make restrictions on yourself through a binding covenant with your magic but when you do that it can have disastrous effects. Voldemort's enhancements are made through this type of ritual as well as Grindelwald and Dumbledore boosts of power before Dumbledore got the Elder wand. part of it is is specific small rituals that have small gains like enhanced strength vitality magic power but also the entirety of The dark arts themselves are, in a way an effect of a ritual.
You see, to be a true dark wizard you need to be able to cast a dark spell such as Severus Snape's cutting charm without it being able to negatively affect you, and the only proven way to do that is to conduct a ritual that minds extremely strong negative emotions and memories to some of your mana creating a secondary form of energy in your body The new energy being Dark mana, and then bind it with regular no-attribute mana to cast a spell turning it into dark spells you can use regular mana for curses but it usually comes out pretty weak and effects dont last long but even the most simple curse with dark mana can last for days.
The reason that dark mana protects a wizard when casting a dark spell is that dark mana absorbs the smaller negative emotions that a wizard generates from casting a dark spell, and so they protect the user from the backlash and achieve a 1+1= greater than 2 effect to the spell, that's why the average dark wizard is more powerful than a standard wizard. Say a regular wizard can send a 100 pounds of force in a standard slicing charm, powerful could probably enough to slice someone without a shield charm but say you need to go through a door 100 pounds of force the average door can probably take 400- 600 pounds of force before caving in the average wizard it would take several casts or a more powerful spell but say they decided to use a dark cutting charm with no dark mana to protect them.
As they are not true dark mages, the spell would affect them if they only did it once, maybe a mild headache, but with each attempt, it would get worse, nightmares, depression, loss of magical control, no control over emotions, eventual loss of magic, Severe Madness and even death. Sooner or later them would become a shriveled-up version of themselves; wizards would lose vitality in the process and die pretty quickly. Witches could actually survive in that state, turning into witch hags. They became creatures similar to vampires, needing vitality from other sources to stay alive.
The power varies for True Dark Wizards; it ultimately depends on how much Dark mana an individual can cultivate. If you need 100 units of Dark mana for a spell, your entire mana reserve is 400. It takes 25 units to cast the dark cutting charm. You cast it 5 times, even though you have Dark mana, one spell is cast, which means the last spell is not protected, and though you won't be affected as badly as a completely average wizard with no dark mana, the negative effects will start to affect you. That's why so many dark wizards are slightly stronger than the average wizard, but very few ever become truly strong. In theory, a top master-level Dark wizard can touch the hems of a Grandmaster-rank Mage. For reference, Dumbledore and Grindelwald were both Grandmaster-rank Mages in their Final battle but Dumbledore had stopped studying the dark arts; he had the extra power of Grandmaster-rank Dark wizard, but his knowledge of dark spells was master rank at most. The Elder wand pushed him to the limit of legendary rank at his best, scraping the bottom of mythical rank. His age had degraded his power to a standard Legendary rank Mage, even with the elder wand, without it, he would be a standard Grandmage
The more powerful you are, the more the boosted effect of dark mana matters, and it's why dark wizards are more likely to reach legendary or mythical rank. To become truly powerful in magic, you must study all the main forms. Dumbledore studied dark arts in his youth, Grindelwald, Voldemort, even rumors that the philosopher's stone was made through messing with soul magic for Flamel. Even Harry from the original story, a case could be made that the reason he was so powerful was that he was getting a small dark boost from the Horcrux, which is why he could cast parcelmagic. Though the average dark wizard is indeed stronger, a strong wizard is a strong wizard. A lazy dark wizard who is at the level of an Advanced-rank wizard like Peter Pettigrew, who barely knows a handful of spells, could never face a top master rank wizard like alastor moody or or some such legendary light wizard.
6. Enhancement magic: Not commonly used in everyday life, seen as brutish, the basics are taught by old families, but wizards are naturally as strong, fast, and durable as the average muggle. Flitwick is actually a grandmaster at enhancement magic which also contributed to his dueling championships; most under master rank struggle to use outward magic and simultaneously enhancement magic. Most well-respected wizards have at least basic understanding of it.