Wonderful question – and one that has tripped us up at least once in the past. (Yes the Mighty Oz, um Ochef, makes mistakes from time to time.)
Cream of tartar is a weak salt derived from tartaric acid, when it is half-neutralized with potassium hydroxide (hence it's other catchy names: potassium bitartrate and potassium hydrogen tartrate). Cream of tartar is therefore an offspring of tartaric acid.
Tartaric acid is not called for very often in the home kitchen – when it is, it is primarily to provide extra tartness to foods. In the recipe you mention, its addition is to give the flatbread a little extra zing. If you don't have tartaric acid on hand (which is much harder to find and more expensive than cream of tartar (which itself is hard to find for so many of our readers)), you could probably use two teaspoons of cream of tartar in place of one teaspoon of cream of tartar and one of tartaric acid.