walks around, pokes with a ten-foot pole
In practical terms, it appears that "magic" is unexplained causality. Drinking willow-tree bark to cure your headache is magic until acetylsalicylic acid is isolated. Burying a copper tablet in your fields (being careful not to use invocations) is magic until astronomy concludes that Venus does not in fact influence it, and the copper will not attract such influence. At which point it gets divvied up into Science (which is reliably reproducible) and at best Superstition (which doesn't work) and at worst Sorcery (which is trafficking with spirits in a coercive manner).
That's another usage of magic, right there. Trafficking with spirits. Which is why both ancient Rome and ancient Greece considered magic impiety. (The biggest witch hunts on record occurred in the Roman Republic.) And in Egypt, magic was freely practiced -- and documented -- as coercing the gods with threats of force. (Riordan got the difference down pat in Percy Jackson and the Olympians vs. The Red Pyramid.) Except that this is kinda a tangent since trafficking with spirits is not the common use in fantasy literature. Sure you get some Evil Cults in sword and sorcery as well as Evil Sorcerers but it's a small proportion even there.
So, back to the main subject, which is that magic is unexplained causality does have a certain amount of utility in looking at fantasy even if Vimes disapproves:
But it does have a certain amount of problems, too, as magic in fantasy novels often is explained. Kinda. One could say that it uses things that were thought magic once upon a time. Most often it uses the handiest trappings -- say, wands, and magical words. (In the ancient world, they thought using even more ancient languages was magical because the gods like to be addressed in unchanging language, which imitates their own immortality.) Some of them go further and use principles of Similarity and Contagion, which indeed underlie a lot of superstitious practice. Poul Anderson plays this quite well in Operation Chaos, even explaining the unusual languages used: basic principle of Similarity, you can not expect extraordinary results from ordinary language. In Lord Darcy mysteries, a wizard fulminates about how superstitious people go to these crude, untutored witches who will treat heart disease with foxglove, which has no symbolic relationship to the heart at all; he, and all the others, use the properly worked out laws of magic.
Then other ones propound this rule or that. Often just to have a rule to make their story tick, with foreshadowing and dramatic tension and all that fun stuff, which can be real hard to do when the magic is completely unexplained. But it's still magic, though having no roots in any practice ever called magic in the real world. . . .