One of the difficult things about discussing magic is that people tend to use the term to mean very different things. If you went and read any of the links above you'll have a sense of the direction I'm heading in with this, but it's still worth clarifying.
Some people use the term in a religious sense - a meaning that's often analogous to the more mystical conceptions of prayer. These people often continue Aleister Crowley's convention of using the spelling "magick" to distinguish between their practice and stage magic. I think this is a false dichotomy, as the kind of magic I'm talking about has more in common with stage magic than you might think.
Aside from that, I think this definition is about halfway right. The primary problem is that in thinking of magic in a spiritual or religious sense (as opposed to, say, a practical or political sense) there's a tendency to follow on from that into constructing yourself a colourful cosmology and/or complex moral dogma - and from there you simply start building yourself a new and temporarily more interesting Black Iron Prison to live in.
People of an aggressively atheistic persuasion, on the other hand, tend to use the term "magic" to label beliefs or practices they consider to have no logical grounding. Again, this contains a flash of insight into the way magic works, but because it's couched primarily in a dismissive mode (and thus contains precisely the kind of cognitive bias that a good skeptic should be striving against) it's ultimately self-defeating. There is indeed a cognitive error known as "magical thinking", and it is indeed related to the actual practice of magic - but it's not the same thing.
Magical thinking is the habit of building non-existent causal links between things in your mind, particularly when those causal links prevent you from challenging your own values or assumptions.
I take a folk remedy for a minor ailment, that ailment clears up and I therefore assume that the folk remedy is efficacious. The problem in this case is that because my ailment was so minor, it might well have cleared up by itself, and though the remedy might have made me feel better at the time, there's no evidence that the remedy in question is more effective than any other placebo. If I were aggressively anti-scientific in my outlook, then it would be very tempting at that point to decide that people who decried my remedy of choice had some other agenda or had been deluded by some sort of conspiracy.
Something bad happens to someone I love - perhaps a medical emergency of the sort that sometimes happens without being predictable. The plain truth is that sometimes awful things simply do happen out of the blue to people who do not even remotely deserve them, and that those things are quite often nobody's fault*.
It is tempting however, to go looking for contributing factors - and the ones that are most often seized on are those with some sort of temporal relationship to the terrible event in question. Something that happened immediately before the event is a good candidate. I might then go on to become a crusader against the thing that I have decided "caused" my loved one's accident**.
So if these things aren't magic - what is? Magic, in the sense that I want to talk about it means the art of understanding and manipulating the relationship between perception and reality.
And we'll talk more about that next time...
*I suppose if you buy into the convention of referring to the-world-untamed as "Mother Nature" you could blame her, but she is a somewhat unsatisfying object of anger.
** The same impulse comes into play when loved ones misbehave in ways that aren't foreseen: cf. school shootings in the US and the corresponding panics about heavy metal music and violent video games.