The words are often interchangeable. In my experience there's a slight difference in meaning between the words around the point where you change phases or stages. If there's a dramatic change, "stage" is more often used. For example, in a rocket destined for space, the difference between stage 1 and stage 2 is dramatic. Often physical chunks of the rocket are jettisoned and entire new engine is primed and fired. If the change is more subtle, "phase" gets used more often.If a mall is trying to gather more interest, they may develop a plan in phases, rather than stages. At the end of phase 1, they want to smoothly transition into phase 2, as opposed to dropping everything they'd done correctly and moving on to something new.
In short, when you change "stages" it often implies that you're changing what you're doing. Changing "phases" often implies that you're just changing focus, but continuing what you were doing -- the idea is that eventually the changed focus will change what you are doing, but its more gradual that way.
As with all words, these are not 100% guarantees, but rather vague hints as to what was intended when an author or speaker chose the word.