Oh, baking soda is different from baking powder. Baking soda is a base (sodium bicarbonate), which is generally added to a recipe that already contains some acidic ingredients. The chemical reaction creates carbon dioxide bubbles that lighten the cookie.
Baking powder is basically baking soda plus some acids, so you don't need extra acidic ingredients to get the leavening effect.
With cookies, substituting baking powder for baking soda usually makes the cookies just a bit more cakelike. The extra acid increases the temperature at which the batter hardens somehow, so it allows the cookies to expand more before their shape is fixed. Do you prefer your cookies fluffy?
Oh, and you think these cookies are bad for you? Consider shortbread. I never realized it until I made it for the first time. You pretty much make a dough by combining sugar and butter until it's homogenous! That's right.
Then you add the flour to what is already a cohesive "dough."
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