потом is an adverb that shows sequence of events. позже is a comparative form of the adverb поздно - late.

Потом also means after or then Позже also means later When used as a one-word reply usually there is no difference.

These words are interchangable in most cases.

Another usage of English "Later" is when you use it with a post-position "on". I am not sure about this, but watching native English speakers using this "Later on" construction, I come to a conclusion that the Russian equivalent to it is often the word "впоследствии". Google translate proposes "в дальнейшем", which I find the same when in regards to future. Here are a few examples. And he, as it turned out LATER ON, is a very friendly person. И он, как оказалось ВПОСЛЕДСТВИИ, очень дружелюбный человек. И он, как оказалось ПОТОМ, очень дружелюбный человек. He told he was right, but, as we will see LATER ON, he mistook. Он говорил, что был прав, но, как мы увидим ВПОСЛЕДСТВИИ, он ошибался. Он говорил, что был прав, но, как мы увидим В ДАЛЬНЕЙШЕМ, он ошибался. Он говорил, что был прав, но, как мы увидим ПОТОМ, он ошибался. This is close to: He told he was right, but, as we will see SOON, he mistook. Он говорил, что был прав, но, как мы ВСКОРЕ/СКОРО увидим, он ошибался. I thought I lost my pen, but LATER ON I found it in my suitcase. Я думал, что потерял свою ручку, но ЗАТЕМ/ПОТОМ я нашёл её в своём портфеле. Я думал, что потерял свою ручку, но ВПОСЛЕДСТВИИ я нашёл её в своём портфеле.

So the conclusion is the following. Позже = Later in the comparative sense, like event B is later than event A (he came LATER THAN me). Позже = Later like "not now", "another time", "in the future", "soon" -- postpone till some indefinite future. (remember the ice-cream example). A bit of official shade. Потом = Later like "not now", "another time", "in the future", "soon" -- postpone till some indefinite future. (remember the ice-cream example). Not official, totally neutral/universal. Потом = Later like "then", or "next" ("woke up, then took a shower" and "what happened next" examples). Затем = Later like "then", or "next" ("woke up, then took a shower" and "what happened next" examples).