If you remember your elementary school volcano experiment correctly, when you mix baking soda and an acid like vinegar, you get a bubbly eruption. When you add baking soda — also known as sodium bicarbonate — to a recipe with an acid (yogurt, buttermilk, lemon juice, cream of tartar), the same chemical reaction occurs and you get carbon dioxide bubbles. Those bubbles help your cake rise and become fluffy.
Note — many recipes that use this leavening method call for buttermilk. If you’re out of buttermilk (or abstain from dairy), by the way, you can make an equally good alternative by squeezing lemon juice into soymilk to create a vegan substitute.
Baking powder, on the other hand, is baking soda with an acid (like cream of tartar) already mixed in. Unlike baking soda, which has a bitter taste, baking powder has a neutral taste so it’s used in recipes where there is no acidic ingredient (or at least not enough of it).
Another good tip: If you’re out of baking powder, you can make your own by mixing two parts cream of tartar to one part baking soda.
As for “cream of tartar,” interestingly enough, it’s a byproduct of making wine! Cream of tartar — also known as potassium bitartrate — is an acidic salt made during the fermentation of grape juice in wine casks. It’s used to stabilize egg whites (which is why you’ll see it added to meringues) and as the acid in recipes using baking powder.