A quick read of the ingredients list is revealing, for an introduction.
Baking soda is sodium bicarbonate, also known as sodium hydrogen carbonate, the monosodium salt of carbonic acid, and bicarbonate of soda. By any name, the chemistry is the same. Baking soda has the chemical formula NaHCO3.
Baking powder is a mixture. The ingredients may vary between products, but looking at my generic can from the grocery store, here is what I see:
Bicarbonate of Soda (Baking Soda!)
Sodium Aluminum Sulfate & Acid Phosphate of Calcium
(That’s NaAl(SO4)2 & CaHPO4 respectively.)
For starters then, the difference is that Baking Powder is a mix of baking soda with other chemicals. To further explore the differences, we shall have to consider the kitchen chemistry aspects of each.
Baking soda behaves as a weak base in water. I expect that most readers are familiar with vinegar and baking soda volcanoes. Vinegar, of course, is a weak acid (thus the sour taste). When baking soda reacts with an acid, it produces carbon dioxide gas. In baked goods, that gas causes expansion within the dough, making the product rise. Without the carbon dioxide, breads, cakes, cookies (etc.) would be denser and flat. When baking soda is used in a recipe, some weak acid is generally added separately, to generate the gas.
Baking powder has an acid already in the mix. In my can, the last two ingredients are acids. Since both the acid and the baking soda are in a solid form, no reaction takes place until the powder comes into contact with water. A little moisture is enough to let the two begin reacting, which would weaken the baking powder’s potency, so the other ingredient (corn starch) is added to absorb moisture and keep the acids and baking soda dry. (Corn starch acts as a desiccant.)
Baking powder and baking soda fulfill a similar purpose in the kitchen, but there are differences as well. In particular, baking powder is largely inert material (corn starch), so a spoonful of it will not be able to produce as much gas as a spoonful of baking soda. It is for this reason that recipes that require only a little “lifting” action, like cookies, will often rely on baking powder. In terms of lifting power (the amount of gas produced), an equal amount of baking soda can do more, so long as the baker remembers to add an acid ingredient as well. It should be noted that because the two behave differently, one cannot be substituted for the other in recipes. If only I had known that years ago!