Dissatisfied means to be unhappy with something; unsatisfied means to be not fully satisfied. Investors may be dissatisfied with their financial returns; debt is unsatisfied if the borrower fails to pay in full. Only unsatisfied may be applied to inanimate things, as shown in the prior example.
The two terms may often seem interchangeable, though they maintain nuanced differences. A diner left hungry may be both dissatisfied (regarding expectations) and unsatisfied (regarding appetite), though the latter would be better-worded as the diner’s appetite, rather than the diner, being unsatisfied.