“What does a CT scan show that an x-ray cannot?”

A traditional x-ray sends energy through the body in one direction to get a single view of the body part. It allows evaluation based on density, so you can see bones separate from soft tissues or air, however many organs have similar densities and cannot be evaluated well with a simple x-ray.

A CT sends x-rays through the body in multiple planes which allow a much better evaluation of the internal organs. In addition, because it is digital information, the images can be manipulated to better differentiate and characterize internal body parts despite similar densities.

A lot more detail.