There are many differences; where the magical power source comes from, who can use what, Black Magic (capitalized), what you have to do to make magic take effort, whether or not it requires ingredients, whether or not it requires a wand, whether or not it's gender-restricted, whether or not it's illegal, et cetera, et cetera.
When you boil it all down you notice that it's all kind of similar. Pretty much something supernatural happens and it chalked up to magic. Here's the dictionary definition(s) for your reading pleasure.
the power of apparently influencing the course of events by using mysterious or supernatural forces : do you believe in magic? | suddenly, as if by magic, the doors start to open.
• mysterious tricks, such as making things disappear and appear again, performed as entertainment.
• a quality that makes something seem removed from everyday life, esp. in a way that gives delight : the magic of the theater.
• informal something that has such a quality : their seaside town is pure magic.
One of the most important things to take away from these definitions are that magic usually contains some sense of wonder. This is something that some writers tend to forget making magic into this mundane thing which is hardly worth noticing.
It's like how people take amazing things for granted today that a hundred years ago would have been miraculous: People taking a ride from one side of the world to the other on a giant metal bird. Communicating instantly with people who live on entirely different continents. A global network of people who can exchange information almost instantly.
And do you know what we use this technology for? Sending videos of dogs farting and people falling off skateboards.
Sorry about the rant (borrowed from a comedian whose name I forget).
Magic shouldn't be boring but that's how it's portrayed in some books. It's got no snap; it has no crackle.
My dear readers: It has no pop.
As I mentioned in another blog, I find that magic is more satisfying when it's difficult to achieve. To paraphrase Robert Frost, the things worth doing in life aren't easy. I believe that this philosophy should be applied to magic as well.
“But William!” you begin to argue, “I thought Magick was supposed to make things easy! What's the point of writing magic in a story if not everybody can do it?”
I like to think of magic like if you crossed a screwdriver with an automatic shotgun; it's useful as a tool but dangerous as hell and you probably shouldn't let your kids play with it.
I hate seeing stories where every minor character has some kind of godlike magical power. I think it reflects a certain amount of laziness in the mind of the author. I mean, a lot of problems are going to pop up if everyone in the world can teleport at will without any kind of repercussion. This is one of the reasons Harry Potter's brand of magic succeeded; there was always something that could go wrong. Always. If an inexperienced wizard tried to disapparate, they could get stuck in a wall or splinch themselves into different places. These kinds of rules are what keeps magic from being too easy. This brings me to my next point: Accountability.
Just like the real world, most people only follow rules as long as there's a punishment for disobeying them. I learned this as a child, but most people alive today have yet to learn this simple lesson. If you get caught driving too fast, you get a ticket. If there were no police then people would drive as fast as they wanted everywhere (though in some places they already do). Streets would be incredibly dangerous places. When you're writing your story, what's keeping the characters from magically exploding an entire village? Or turning everyone into pigs and frying them up?
Now, I'm not saying that you need to have a magical DMV in your story who annoyingly tightens their grip on all things magic (though that premise might work as the main plot in a story). Let me paint a picture for you.
You've got a villain in your story who is incredibly powerful. In fact, you've only shown him exercising his endless power over every other character. As far as the reader knows, there nothing he can't do. What's stopping him from ripping the planet in two? Or at the very least teleporting into the hero's bedroom and killing him in his sleep? This is where another vital part of magic-making comes into play: The power source.
In video games this is typically called mana. I don't know why it's called that, but it's essentially a pool of magical energy that you draw on for spells. Once you're out of mana, you have to find a way to get it back.
Although it serves its purpose in video games, mana doesn't make as much sense in a story. I guess you could have your characters cry, “I'm out of mana!” after a fight, but to non-gamers this phrase doesn’t make much sense. Authors have a variety of tools at their disposal for giving magic-users a source of magic. They can be almost anything, but the list includes:
Holy power: Usually a thinly-veiled reference to God or angels. Can also be a more abstract “light” that the character receives from on high.
Demonic power: From the spirit world, from demons themselves, or received as a previous bargain made with a demon.
Elemental power: From those four incredibly overused elements, Earth Wind Fire and Water.
Trinket power: From an item or items carried by the hero. This could be their armor, a necklace, a sword, etc.
From-gods power: Think of Hercules, his power is just a “gift” until he angers the gods.
Well of Power: There's a ton of magical energy that is drawn by the character somehow. It doesn't even have to be nearby to be used.
Tradeoff power: The character is incredibly tired afterward, sometimes to the extreme. Or they become dehydrated as they spell, or they age, or someone in their family dies, or their soul is sucked away.
Ceremonial power: This is the kind of crap that I detest. I hate reading about seances, chanting, pentagrams or anything else that requires Hollywood Voodoo. Usually used by the bad guys, but sometimes by the good guys. If I encounter this stuff in a book, I will deeply consider stopping.
Then there are stories where it doesn't cost a thing to create magic, it's just very hard for the character to do. Theoretically a person could be so good at magic that they would never have to stop, except maybe for sleep. In Diana Wynn-Jones's books, her characters don't have a limited amount of it, but it's typically very hard. Sometimes it even requires ingredients or a ceremony or something. It's so hard to do that people mostly rely on professionals to do it. Even the bad guys sometimes use more conventional means of getting their way (imprisonment, bullying, espionage, murder and so on.)
On the other hand, Harry Potter has a great system where the difficulty of the spell is based upon how hard the wand-motion is, plus a strange Latin word. Later on, we even learned about nonverbal spells, which were almost impossible for most of the characters. Without wands, the characters were completely unable to use magic. I thought this was an interesting tradeoff and it worked well for the story.
The point I'm trying to make is that you need to avoid making your characters superhuman; look at Spiderman: Even with his super-powers, he's still one of the most (relatively) weak heroes in all of comics.
It's seeing him overcome almost impossible odds that make him so endearing (that and his witty banter.)
If you don't follow these suggestions, you risk making your main characters into a Mary-Sue, but that's a topic for another day.