How do a cataract and short-sightedness differ?

Very different: Short-sightedness, or myopia, means that the best vision without glasses is close to you. A cataract is when the natural lens of the eye becomes less clear over time.

2 different things: A cataract is an opacity in the lens of the eye that can blur your vision. Myopia is a refractive error that is corrrectable with glasses in which your near vision is clear without glasses or contacts but can be made clear with the proper eyeglass or contact prescription.