For the most part they are the same and interchangeable. However, in a more refined translation, dissatisfied means more of a negative tone than unsatisfied. Dis satisfied means you really are not happy with whatever the situation is. Un satisfied tends to mean you just did not have your expectations made , so you were disappointed but not actively angry with your satisfaction. Its a subtle difference, so in general they do mean the same thing.

They would mean the same to many people. Dis and un "affixes" attached before English words have the same meaning to reverse or negate. Today unsatisfied is used more to suggests your expectations were not meet. Dissatisfied is used more to suggest you were not happy. "I was unsatisfied with that meal at the restaurant" = it did not meet your expected standards. "I was dissatisfied with the/that meal at the restaurant" = it did not please you. You found it unappetising etc or cold when it should have been hot etc.