The key difference is the size of the image circle. EF-S projects and image circle which is just big enough to cover the smaller sensor of crop format cameras, which is 22.3 x 14.9mm on Canons, less than half the area of full frame's 36 x 24mm.
If you could fit an EF-S lens on to a full frame camera, the image would be a small circle in the middle, with black around the edges. In fact you can fit DX lenses (same as EF-S) on full frame Nikons, and that's exactly what you get.