What's a pan and what's a pot?
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 the etymology of the words put it, pans are shallow (akin to dish, plate) most suitable for shallow frying, and pot is a vessel for boiling, simmering or deep frying.

Note: Like all living things, languages can also evolve and words don't necessarily stay true to their origins. Saucepan should have been called saucepot, but that’s just how languages work; as people coining terms and words don't necessarily put much effort in the history and story of the words.