shortage means there is less of something than there is supposed to be. shortcut means a path one can take to shorten the time it takes to do something. shortwave is a type of radio transmission. shorthand is a type of writing that uses shorter versions of words.

Example sentences to accompany Indigo's answer: Shortage: There was a food shortage during the Great Depression. Shortcut: I don't like the way he works because he takes too many shortcuts. Let's go this way instead, I know a shortcut. Shortwave: Shortwave radios can be used for long distance communication. (from Wikipedia) Shorthand: It's a good thing I can write in shorthand because the Professor speaks quickly.