Magic is usually an integral part of any secondary fantasy world. That tends to be the thing that makes it a "fantasy world", rather than just some form of alternate Earth. But "magic" is a broad, wide-ranging term. What exactly does it mean, and how does it work?
If you're trying to define magic in the simplest, most accurate way possible, the best I've got is "Energy that can be shaped to generate effects contrary to natural order." Which can cover a pretty wide range.
How magic works in your world is a pretty crucial concern, as well as what you call it. Hell, talk to just about anyone about process of writing fantasy, and the phrase "rules of magic" will probably come up. In Thorn of Dentonhill, I call it only "magic"-- at least in what Veranix can do-- and since it's in an academic setting, I name the energy itself ("numina"), but what magic can do in that world is relatively open-ended, so there's little need for a more specific term.
But what marks the line between a mage, a wizard, a witch, a warlock, a sorcerer, a necromancer, etc? Well, necromancer is easy: they deal with the dead. But even that can be open-ended. A necromancer might be raising a zombie-army, or might be investigating the dead and contacting spirits to solve murders.* But are those all things in your world?
But what is "witchcraft"? What is "sorcery"? Are these all just different names for the same thing in your world, or does your world have one of them specifically? Does your world have all of them, as different forms of "magic"?
I've often cited The Belgariad as an early influence on me, and one thing I liked was how he had several different powers in his world, though "magic" and "witchcraft" were limited forms, while "sorcery" was a more direct connection to the source-code of the universe, giving its users immortality and the ability to create something-- including a new species-- out of nothing.
Magic in Thorn of Dentonhill is not so limitless. For one, it can't heal, nor can it touch the dead or the afterlife. (Strictly speaking, a mage could make a dead body get up and walk around, but it would be literally nothing more than puppetry of any inanimate object.) It can't directly affect the mind, or give one the ability to read someone's thoughts. However, in the world of Thorn, there are other powers beyond that of "magic". At the beginning of Thorn, Veranix isn't as familiar with them as he probably should be. He's not exactly the best student, after all.
*- Have you read Amanda Downum's Necromancer Chronicles, specifically The Bone Palace? Well, you should.