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A Super Koopa is a Koopa that has a cape on. Of course, these Koopas can fly in Super Mario World. However Super Koopas don't have shells.
There will be Super Koopas with yellow capes and red capes. If Mario or Luigi hit them, they will fall to the ground and become shell-less Beach Koopas. If Mario or Luigi hit a Super Koopa with a red cape, not only will the Super Koopa become a cape-less Beach Koopa but a feather will appear.