These are the different kinds of miso I know of: regular soybean miso, as well as genmai miso (made out of soybeans and brown rice), kome (soybeans and white rice), mugi (soybeans and barley), hatcho (soybeans and sea salt), and natto (made from soybeans and ginger).
All the above kinds I think, can be found in different colors and strength of taste, it depends on how long they're fermented or aged - from white to dark brown. I believe they cal all be used interchangeably, depending on the exact taste you want.
White miso is the lightest in taste and color (obvioiusly).
I like it in soups, salad dressings, and sauces.
Yellow miso is also light in flavor, but it's saltier.
Red miso is strong and salty and (this is quoted from the label) "...is generally used for stews, soups and braised foods". I use this one the most because I like the stronger flavor.
Dark brown miso is the most strong. I don't think I've ever used it.