Fairly frequently, the disputes I run into over the validity of witchcraft happen because one side or the other has conflated magic with 'magical thinking'. 'Magical thinking' is the idea that if you just believe in something enough, it will come to pass. You can visualize that weight loss without ever cutting a calorie, wish your way into that loving relationship without working on communication, and believe that a better job is coming instead of working at the one you have.
People on both sides of the faith debate seem to buy into this, and so non-practitioners become confused when people who practice more practical forms of faith-based work refer to it as 'magic' or even 'prayer'. So allow me to explain the difference, as I see it, between magic and magical thinking.
I'll use a story to illustrate it. Several years ago, on finding out that I'm a witch, one of my friends asked me to do a spell to help him get a new job. He hated the one he had, he said. I told him to spend half an hour writing out a list of the general criteria he wanted in a job, and to bring me that and a copy of his updated resume. He arrived with a listing he'd printed out from a job website, and explained that he wanted me to do the spell to get him THAT job. I said that no, that's not how it works, and asked him about the resume. He hadn't had time, and besides what did I need it for? I explained that I was going to use the resume as a focus, to create a spell asking that when he applied for a job, his resume would reach the desk of the person most likely to hire him, be seen by the right eyes and represent him well. Basically, I was offering to use magic to remove obstacles and allow him to more easily get the right job for him.
I will never forget the look on his face when he said, "What do you mean APPLY?" Yes, honey, you have to actually APPLY for the jobs, and go to the interviews. You can't just wish for it and believe hard enough that you should have it, and expect it to happen. You can't just buy a witch a piece of pie and sit back to let job offers rain upon your head. If it were that easy everyone would do it that way. And I would have SO MUCH PIE.
He'd fallen prey to magical thinking, because he believed that if he focused on a thing, wanted it enough, wished for it, then it would 'just happen'. Magical thinking is based in a sound principle, the first thing they teach you in driver's education: where the eye goes, the car will follow. However, it completely ignores the mechanical connection between eye and head, head and body, body and hands, hands and steering wheel, steering wheel and car. According to magical thinking, the eye controls the car and no other effects have to follow through. You don't need any understanding of the process of driving, because the only thing that matters is where you focus your eye. You don't even need to gas up the car or turn it on. Just keep *looking* at where you want to be, and someday you'll just be there without crossing the intervening space.
There's a good deal of evidence that focusing on positive outcomes improves your life experience. Thinking about what you want, instead of what you don't want, increases the chances of getting what you want. Lots of people make ridiculous amounts of money hosting workshops and writing self-help books that expound upon this premise -- and stop there, creating a class of frustrated self-actualized theoretically empowered people who still don't understand why they're not getting anywhere.
Actually acting to *get* what you want increases those chances even further, and that's where practicing magic comes in, and that's the part a lot of people (pagans, Christians, and atheists alike) don't want to talk about.
For me, magic is best described as "an act of will backed by the will to act." It's a bargain you make with yourself and whatever divine entity you're petitioning. You say to the entity, "If you will act upon the world to assist me, I will commit to the technical part of the process and do the physical work."
If I want a new job, I'll polish my resume and apply for jobs. If I want a new romantic partner, I'll actually ask people out. If I want better health, I'll improve my habits. That's my part of the bargain: the daily work of what I want. Driving the car.
Sooo...where does magic come into it?
Luck. Intuition. Coincidence. Reinforcement.
Nothing is assured. I know people who work hard, do all the right things, perform every right action to get to what they want, and they don't get it. A flat tire on the way to an interview means they miss out on a job. They don't notice the attractive person sitting at the next table reading their own favorite book. They turn left, instead of right, and miss out on an opportunity. I know people whose doctors have made bad decisions, with terrible consequences.
When a friend goes into surgery, I know the gods aren't holding the scalpel. But do I believe they can be the voice of intuition that helps a doctor make a wise decision. They can be the second glance a nurse takes to see that a medical dosage was written down wrong, confirm the number and get the patient the right treatment.
I have asked the gods to be the voice that whispers to me "refresh that jobs listing one more time before you log off," so that I didn't miss applying for a great job. To inspire me to try a new coffeehouse or restaurant and strike up a conversation with the attractive man whose table I ended up sharing. To help me find the strength and focus to keep acting towards what's important to me, even when I'm exhausted and demoralized.
Magic smoothes the way. You still have to travel the distance. That's the difference between it and magical thinking. Magical thinking genuinely believes that you can convince whatever forces direct the Universe to give you a miracle every time you want one, with no investment or work on your part.
As a famous squirrel taught me when I was but a child, that trick never works.