съесть - to eat up (a whole apple or w/e)
поесть - to eat a bit/some amount of something

There are way more differences than these two above. In other words, there are differences.
At the moment I am satisfied with these. I don't think I will be able to memorize more uses.
So
1. Я поел один бутерброд - I haven't finished it. I just bit some pieces of the sandiwch
2. Я съел один бутерброд - I ate it all!