Question: what are the differences between various types of flour?

The main difference seems to be protein content. Lower content = fluffier, higher = chewier.
Cake flour has less protein than bread flour and all-purpose flour falls somewhere in the middle.
Self rising flour has baking powder and salt mixed in.
Bread flour has more gluten- which helps the yeast work better.
All purpose flour is lower in gluten and slightly lower in protein. You can substitute one for the other, but all-purpose flour won't rise as well as bread flour.

From the Wheat Foods Council:

All-purpose flour is the finely ground endosperm of the wheat kernel separated from the bran and germ during the milling process. All-purpose flour is made from hard wheats or a combination of soft and hard wheats from which the home baker can make a complete range of acceptable backed products --- yeast breads, cakes, cookies and pastries.
Enriched all-purpose flour has iron and 4 major B-vitamins (thiamin, niacin, riboflavin and folic acid) added in amounts equal to or exceeding that in whole wheat flour. Actually, all enriched flour has twice the folic acid as does whole wheat flour. All but about 5 percent of white flour in the United States is enriched.

Bleached all-purpose flour is exposed to chlorine gas or benzoyl peroxide to whiten and brighten flour color. Chlorine also affects baking quality by "maturing" or oxidizing the flour, which is beneficial for cake and cookie baking. The bleaching agents react and do not leave harmful residues or destroy nutrients.

Unbleached all-purpose flour is bleached by oxygen in the air during an aging process and is off-white in color. Nutritionally, bleached and unbleached flours are equivalent. But bleached flour is beneficial for cake and cookie baking.
Bread Flour
Bread flour, ground from the endosperm of the hard red spring wheat kernel, is milled primarily for commercial bakers, but is available bleached or unbleached at most grocery stores. It is usually enriched. Although similar to all-purpose flour, it has greater gluten strength and is generally used for yeast breads.

Self-Rising Flour
Self-rising flour is an all-purpose flour with salt and leavening added. One cup of self-rising flour contains 1 1/2 teaspoons baking powder and 1/2 teaspoon of salt. Self-rising can be substituted for all-purpose flour in a recipe by reducing salt and baking powder according to these proportions.

Cake Flour
Cake flour, milled from soft wheat, is especially suitable for cakes, cookies, crackers and pastries. it is low in protein and low in gluten.

Pastry Flour
Pastry flour has comparable protein, but less starch than cake flour. It is milled from a soft, low gluten wheat and is used for pastries.

Gluten Flour
Gluten flour, processed from high protein wheat and containing much higher protein than bread flour, is used by bakers in combination with low protein or non-wheat flours. The gluten flour improves baking quality and produces yeast breads of high protein content.

Vital Wheat Gluten
Vital wheat gluten is derived from wheat flour and is the texture of flour; it is concentrated dried gluten protein with very little starch remaining.

Semolina
Semolina is the coarsely ground endosperm of durum wheat. high in protein, it is used by American and Italian manufacturers to make high quality pasta products such as macaroni and spaghetti. It is also used for couscous in Africa and Latin America.

Durum Flour
Durum flour is a by-product in the production of semolina and is used for American noodles, some types of pasta and occasionally in specialty breads.

Whole Wheat Flour
Whole wheat flour is a coarse-textured flour containing the bran, germ and endosperm. The presence of bran reduces the gluten development, therefore, bake products make from whole wheat flour tend to be heavier and denser than those made from white flour.

Whole wheat flour is rich in B-vitamins, vitamin E and protein, and contains more trace minerals and dietary fiber than white flour. It also contains about five percent fat. In most recipes, whole wheat flour can be mixed half and half with white flour. Graham flour is another term for whole wheat flour.

Farina
Farina is the coarsely ground endosperm of hard wheats. It is the prime ingredient in many hot breakfast cereals. it can also be used for pasta.