When I was in culinary school we were given product ID tests, and the most difficult one, by far, was a flour test orchestrated by the baking instructors during the second round of baking classes. Repeating rows of mis en place cups were lined across the steel prep tables, each one containing a different type of flour. These were not miniature archeological tells of buckwheat or corn flour, but small piles of white flours–pastry flour, bread flour, all-purpose flour, cake flour–spread anonymously across the immaculate buffed metal, as if it were Pablo Escobar's private Medellín pastry kitchen.
This may seem capricious, even cruel (it did to us; we all failed), but there was a purpose to it. Pastry chefs need to be able to distinguish flours from each other: what if the bags are switched, unmarked, or just too confusing in the rush of a professional kitchen? At home you may not have a tart production line, but there's still a value to knowing your flours and how they work, and being able to understand the subtle differences between them, particularly if you don't have the specific flour a recipe calls for.
So what's the difference? Unbleached all-purpose (or AP) flour is the standard flour in most kitchens and is a highly versatile (hence the name) flour that can be used in most recipes. Depending on the brand, it can have have a protein content of between 8-12%. The protein content is relevant because, among other things, it determines how much liquid the flour absorbs.
Bread flour is similar to all-purpose but has a higher protein content (11-14%) and more gluten; it's so called because the higher amount of gluten helps build the structure that many breads want and need. Cake flour, which is bleached, has a lower protein content (around 8%) than all-purpose. Pastry flour also has a lower protein content (about 9%) than AP flour and is very finely powdered. Both cake and pastry flour have less gluten than bread and AP flour, and so build a finer, more delicate crumb.
Although very similar in appearance, these flours have subtle qualities that can make a surprising amount of difference to baked goods. And then there is the vast multi-cultural world of whole grain flours, which is an entirely different post; at least they're easier to identify. A note about measuring flour: do not pack your flour, but scoop the flour in the bag a few times to lift it a bit, then scoop it up with a measuring cup and level it off with the back of a knife. As this is somewhat imprecise, most bakers and pastry chefs measure their flour by weight.
Can't find the right flour? King Arthur Flour, the employee-owned Vermont flour company founded in 1790, has a terrific website where you can buy most kinds of flour. They also have a bakers' hotline, a bakers' blog, free online classes and recipes.
King Arthur Flour: 58 Billings Farm Road, White River Junction, Vermont; (802) 649-3717.