From the Gamma World rulebook:
A short rest requires about 5 minutes. During a short rest you renew your encounter powers, refresh your Alpha Mutation(s), and regain all your hit points. You can take as many short rests per day as you want.
An extended rest requires at least 6 hours, and you must rest or sleep during this time. You can take one extended rest per day. At the end of an extended rest, you regain all your hit points, recharge your encounter powers, and refresh your Alpha Mutation(s). You also need to take an extended rest before you can advance to the next level.
Apart from the requirement for leveling up (and the time needed, obviously), I can see no difference between a short and an extended rest. Am I missing something?