I think the answer to your question lies in the etymology of the words.
Pan is actually coming from Germaic pfanne (in Dutch panne).
Which is from Latin patina (shallow pan, dish) and Greek patane (dish, plate).
On the other hand, pot also has Germanic roots it means vessel (also in Dutch) coming from pottus (drinking cup) for Latin.
So the difference as ...
As a native English speaker, certainly where I come from, saucepan and cooking pot are mostly interchangeable. However, I understand the differentiation to be that "pans" have long, extended handles and "pots" do not. So a pan:
And a pot:
Edit to include dictionary definitions kindly provided in a comment by user3169
Pan: "A pan is a round metal container ...