The two words overlap but they are properly used in different contexts.
If a person has ordered 20 boxes of tiles to tile a floor and finds that they are not sufficient to cover the whole floor, that person is short of one or more boxes. That's to say that more are needed.
If a supplier has an order from a buyer for 20 boxes of goods and only delivers 19 boxes, then there is one box short. That's to say that the delivery is incomplete.
However, if the supplier delivers all 20 boxes and the retailer later finds that there are only 19 boxes where there should be 20, then there is one box missing. That's to say that a box has disappeared.