The first difference you should know is that "потом" is only a simple adverb ("later", "then") while "позже" is a comparative that can can also tell you "later than what" the even happens. Second, "позже" implies that, probably, some time passed between the actions. Doesn't work if the actions follow one after another.
Use "потом" when talking about the sequence of actions.
Use "потом" or "позже" referring to "sometime later" («Потом поговорим!»="We'll talk later").
Use "позже" when you need a comparison relative to something else ("Я пришёл позже тебя", "Урок начался на пять минут позже").
Note also that at the beginning of the sentence the use of "позже" instead of "потом" in a sequence of events sounds slightly bookish ("Позже я отправился в парк"). At least, I probably woulnd't use it in my speech like that. And, of course, it means that some time passed.