A shortage means that something is running low, such as a shortage of water during a drought. A shortcoming is a deficiency (either in personality, when talking about people, or in functionality when talking about things). For example, laziness would be considered a shortcoming. In terms of things, if you buy a phone that can't take pictures, for example, that might be considered a shortcoming.

Shortcoming is like flaws or something that you are lacking of

Shortage is something that is insufficient in amount