Do the terms non-weighted and semi-weighted mean the same thing for MIDI keyboards? If they are different, what would be the difference?
They are different.
Non-weighted keyboards are based on springs, so the feel is very different from the keys of a piano. Weighted keyboards have counterweights or resistance on the spring to mimic the feel of a real piano. Semi-weighted is somewhere in the middle, they have counterweights or resistances that counter the springy feel of the keyboard, but the weights are not as heavy as in a fully weighted keyboards.
The feel of a non-weighted keyboard is springy, like most MIDI keyboards (specially the cheap ones) are. Semi-weighted feel is between a real piano (what fully weighted is supposed to feel) and a non-weighted keyboard.
If you want to mimic the feel of a real piano as much as possible, you go for fully weighted keys or hammer action keys.
If you want the feel of an old synth, or "spring" feel, you go for non-weighted.
If you want a feel that's between weighted and non-weighted, you go semi-weighted.
More about the pros and cons in this previous question: What are the practical advantages of keyboards with non-weighted keys vs. weighted hammer action?