What is the difference between fuel exhaustion and starvation?
Fuel exhaustion means there is no more fuel on board the aircraft. Fuel starvation means there is fuel somewhere, but it isn't available to the engine(s) for any one of a number of reasons: pilot error, blocked fuel lines or valves, malfunctioning fuel pumps etc. You can read a study of exhaustion and starvation incidents here.

A "fuel shortage" isn't a formal aviation phrase as far as I know, but "minimum fuel" is a formal phrase with a specific meaning. This is from the FAA's AIM 5-5-15:


  
  Advise ATC of your minimum fuel status when your fuel supply has reached a state where, upon reaching destination, you cannot accept
  any undue delay. 
  Be aware this is not an emergency situation, but merely an advisory that indicates an emergency situation is possible should any undue
  delay occur.
  On initial contact the term “minimum fuel” should be used after stating call sign.  
  
  EXAMPLE− Salt Lake Approach, United 621, “minimum
  fuel.”
  


This question has some more information.