Stay order is basically a court order that suspends the legal proceedings from further occuring. Whereas, Injunction is a court order that refrains a party to do something to prevent further harm or loss.

A stay order is a court order directing the stay of proceedings. Usually takes place after a higher court who is approached with an appeal or revision directs the lower court to stay proceedings from further taking place. It is an order directing a court whereas Injunction is an order directing a party either from doing something or refraining from doing a thing.