What is the difference between various types of flour?

The difference is the amount of protein contained in the flour which can range from 5% to 15%. Bread flour usually has a minimum of 12% because bread needs it to rise properly. Cake flour has lower amount of protein, and all-purpose is in the middle.

See also here. The link at the bottom opens a table of the different protein ratios for the different products it is used for.

Chef Darin Sehnert, of chefdarin.com and the teaching chef at a cooking school in Savannah, GA, has a great in-depth article on the various types of flour:

https://web.archive.org/web/20120103014449/http://www.chefdarin.com/2009/08/flour-power

He answers questions such as "Why and when to use cake flour" and "Why and when to use all-purpose flour." It's a long read but does a great job of exploring the different types of flour.

Cake flour has a lower protein content than AP flour. It's essentially the opposite of bread flour (higher protein content). You can add protein (turn AP flour into bread flour) in the form of vital wheat gluten to increase the protein content of your flour, but I don't know of any way to go the other way around. Some brands of AP flour from the southern US are "softer" and could probably be used as cake flour. "White Lily" is one of these.

Cake flour has less protein than AP flour which has less protein than bread flour. Cake flour is sometimes ground finer. The wheat used is known as soft (cake) or hard(bread) or a mix...the goal being to achieve a certain protein level. Professional bakers will care about this more than you need to.

No, you can't turn AP flour into cake flour, but you can, pretty much, use AP flour instead of cake flour. The cake MAY potentially be a little tougher/firmer, but you probably won't notice the difference.

Having cake flour around won't mess you up, if you make biscuits regularly, for instance, since soft flour is better for biscuits, which you definitely don't want to be tough. But if you just want to make this cake, substitute AP for the cake flour and you should be fine. If it calls for beating it for a long time after you add the liquid, you might cut back on it a bit, so that you develop the gluten a little less (more protein can build more gluten...see bread flour above), but most cakes don't call for a whole lot of beating anyway.

One element of the question that hasn't yet been answered: "Is it really necessary to stock 3 types of flour in my pantry...?"

Probably not. At least two are good, but it will cost you more than just buying AP. You can actually blend your own all-purpose flour by mixing a soft flour (like cake or pastry flour) and a hard flour (like bread or "high-gluten" flour). Many professional bakers take this route. I have entire cookbooks where all recipes specify mixtures of two types of flour, usually bread flour and pastry flour. "All-purpose" does not exist, and you tailor your blend to the specific purpose of the recipe.

Speaking of which, as alluded to in other answers, not all "all-purpose" flour brands are created equal. Gold Medal probably falls around the middle, while King Arthur all-purpose is harder and closer to bread flour. White Lily all-purpose is softer and closer to cake flour.

There are also further subdivisions than three. Most commonly, I've seen a five-fold division. Going from softest to hardest:

1. Cake flour: from soft wheat, very soft and light, essential for very light types of cakes with feathery and downy textures. Often bleached, not just for color but chemically it makes the flour softer than otherwise possible.
2. Pastry flour: quite soft and low in gluten (also from soft wheat), but not as much as cake flour. Good for pastries, biscuits, cookies, quick breads, pancakes, other tender baked goods. Not normally bleached. (White Lily is close to this.)
3. Normal "All-purpose" flour: blended from various wheats, not really great for anything. Not terrible at anything either. National brand flours (like Gold Medal) fall into this category.
4. Bread flour: made from hard wheat, better for making breads, rolls, and other things that depend on a yeast rise. Doughs will rise higher, resulting a in a lighter loaf. Will also result in a tougher product unless the dough is tenderized by including things like fats/oils or milk. King Arthur all-purpose flour is close to the "bread flours" marketed by regular brands like Gold Medal. King Arthur bread flour is even higher gluten.
5. "High-gluten" flour: made from hardest wheats, these are specialty flours, predominantly used by professional bakeries. They have an even higher gluten content than standard bread flour -- the highest possible from normal wheat (without isolating gluten separately and concentrating it). High-gluten flours are essential for very chewy things like bagels and chewy pizza (though some prefer a lower gluten flour for a more tender pizza crust). They also can be added to whole-grain bread doughs with heavy ingredients to provide enough lift to get a light or sandwich-style loaf.

For a while, I only tended to stock high-gluten and a very soft pastry flour. I could then create any other flour in-between by blending these two in whatever quantity was appropriate to the application. That's effectively what all-purpose flours do anyway, so this gives you more control. I haven't done this for a while, because I've moved away from the place I could buy specialty flour in bulk 50-pound bags for reasonable prices (and I've moved away from the people I used to share these purchases with). Things like pastry flour and high-gluten are so expensive and generally available only for mail order, so the home baker is stuck with the options in the grocery store. (By the way, I personally avoid most cake flours because of the bleaching, which can also affect the flavor of the flour -- a good-quality soft pastry flour is almost always sufficient. "Unbleached cake flour" that you sometimes see these days is usually pastry flour in terms of strength.)

I haven't discussed here the various types of whole-wheat flour, which seems like a different question. Whole-wheat is naturally high in gluten, often even higher than bread flour, but because of the additional bran and germ elements, it doesn't tend to rise as high or produce results that are as chewy as bread flour. Various size grinds and different levels of "extraction" (i.e., what size particles are taken out, how much of the whole-grain elements are removed) make various brands of whole-wheat flour seem very different. And then there are things like self-rising flour... just don't do it (in my opinion). Add your own leavening if necessary.

Finally, it should be noted that this classification only goes for the United States. Similar sorts of flours exist in Europe, for example, but different types of wheat and different processing can yield further variety in other characteristics of the flour. This is just a continuum from soft/tender to chewy. But by varying things like ash content, moisture content, etc., you can change other characteristics of the flour, like how much water dough will absorb, etc. without changing the tender/chewiness factor as much. So Europeans end up with types of flours that can do things differently from what American flours do.

I think it is worth mentioning that in the Central-to-Eastern Europe and in other places likely as well, you differentiate 3 basic types of flour according to how fine it is milled:

• 00 flour or smooth flour, used into sauces;
• half-whole flour, for general purposes, especially into most baked cakes;
• whole flour, for making breads and dumplings; it is as well put in a thin layer into a baking tin to prevent burning-on.

It is quite difficult to purchase whole flour in many parts of the world and people don't use it to bake bread there. This makes Eastern-European people quite unhappy about the bread quality all around the world.