You may find people who will say there is a difference, but as an American, I find both fine. I know that there are people who say "A roast may be done, but people are fnished," but even so, "Are you done yet?" and "There! I'm done!" are also very commonly said.
You would use I have finished and Have you finshed? with the example of completeing a job. I am finished can be used. For example, when someone realises that their bankrupt or if they have made a terrible mistake they may say 'I'm finished'.