Friend of The Food Geek, Joe, asks via Twitter:
I'm not sure if there's a firm dividing line between a cook and a chef, per se. In general, there are two things that make a chef: creativity and career.
A chef is someone who is, or at one point was, paid to make food. If you've never cooked food as a career, it's going to be difficult to convince people who really care about the difference to call you a chef. I'm sure there are a couple of paths that you could go without pay and still be called a chef, but those paths are probably only unpaid because you are independently wealthy or otherwise not in need of money and have eschewed all types of paycheck.
Still, that's not quite enough. If all you do you flip burgers at your national chain fast food restaurant, chances are that you aren't going to be called "Chef" if you were speaking at a food convention or similar. At that point, you're more of a line cook. A chef has to be responsible for the soul of the food. A chef should have a deep understanding of how to cook many types of food, what flavors go together, how to handle kitchen equipment (knife skills come in handy here), and so on. A chef should not require the directions part of a recipe, and usually shouldn't require the amounts in a recipe, either.
Deviation from one or the other of those two traits will get you bumped from "chef" to "cook". No matter how much money you make from cooking, if all you're doing is setting a timer and raising a basket of fries into and out of the oil when things go "beep", you aren't a chef. And no matter how well I understand the intricacies of gluten creation or heat transfer, and no matter how many meals I make at home, because I don't make food for other people for pay, I am not a chef.
The distinction of Chef vs. Cook probably got its real start back in the Middle Ages, when guilds of chefs were formed in France, each with different focuses. Eventually, these roles evolved into a proper way to set up a commercial kitchen in France, and many professional kitchens employ at least some of these roles today. You have the Executive Chef, who does menu planning, purchasing, quality control, and a lot of the business work. Saucier makes the sauces, Pastry Chef makes the breads and desserts, and so on. Here is a good description of various chef's roles are they are in use today, but all of these derived from the various guilds from France in the Middle Ages.
Now, all this being said, there are definitely those who like to think that chefs are better people than cooks. Most of those people are chefs. It's not even true that chefs are necessarily better at cooking than cooks. Very often it is, but it would not be hard to find any number of chefs who are not as good at cooking, in general, as any number of amateurs, and if you limited the food to only the specialties of the individuals doing the cooking, there are going to be many more cooks who cook better than chefs.
Being a chef will generally mean that you have a lot more flexibility in what you can make well. It will also probably mean that you can stand for 8 to 16 hours at a time without more than a couple of short breaks. And, most importantly, it means that what you do make, you can make over and over again and have it taste pretty much the same as when you made it 2000 dishes ago. Consistency is vital for a chef, but not necessarily for a cook.