How is shortening different than butter or margarine, regarding nutrition and healthiness? Why the name "shortening"? Does it make cooking time short?

Yes. Shortening can be from animal lard or vegetable fats. Refers to fat that is solid at room temperature. It is called shortening since it prevents cross-linkage between gluten molecules, thereby preventing elasticity. That's why it makes a flaky crust pie or crumbly cookies. It does not make cooking time shorter. It also has a higher smoke point than butter or margarine; good for deep frying.
Chemistry. Fats make pastries less stretchy ("shortening") and more crumbly; by convention, "shortening" is cooking fat solid at room temperature that isn't margarine or butter. Some are artificially hydrogenated producing trans-fats, supposedly unhealthy -- a claim based on people's recollections, with contradictory results, and no good animal model. I'm reserving judgement, though they're mostly gone.