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Airplane wings are made to fly at relatively low speeds (up to 80% the speed of sound) while the space shuttle lands at hypersonic speeds (more than 10 times the speed of sound). They need to be built differently because they have to deal with different circumstances.

The shuttle's wings are short and stunted, called a delta wing, to deal with the shock waves in the air. They don't have any use for takeoff, and do nothing while in space. But they help control the shuttle when it comes in close for a landing. You don't see a very defined airfoil shape, because lift is not needed. 

On the other hand, airplane wings need that curve on top to stay in the air. Learn more about that here.