What is the difference between baking soda and baking powder?

Baking soda is pure sodium bicarbonate, while baking powder includes an acidifying agent (cream of tartar) and a drying agent (starch).

You can substitute baking soda for baking powder if you already have an acidifying agent in a recipe (like buttermilk).

http://chemistry.about.com/cs/foodchemistry/f/blbaking.htm

Normal double-acting baking powder makes CO2 (thus giving a rising effect) in two ways: when it gets wet, and when it is heated.

Baking soda only makes CO2 when it gets wet.

From Wikipedia:

The acid in a baking powder can be either fast-acting or slow-acting.[6] A fast-acting acid reacts in a wet mixture with baking soda at room temperature, and a slow-acting acid will not react until heated in an oven. Baking powders that contain both fast- and slow-acting acids are double acting; those that contain only one acid are single acting. By providing a second rise in the oven, double-acting baking powders increase the reliability of baked goods by rendering the time elapsed between mixing and baking less critical, and this is the type most widely available to consumers today.

You can make your own baking powder using baking soda, cornstarch, and cream of tartar.

1/4 tsp baking soda 1/2 tsp cream of tartar 1/4 tsp cornstarch

That will give you one tsp baking powder. Increase as necessary.

Also, if you don't have all those ingredients, you can use 3 measures of baking powder for every measure of baking soda, although you won't get the same flavor profile with the reduction of acidity from baking soda.

In addition to forefinger's answer, I also believe baking powder has cream of tartar in it, making it more pH neutral.