No difference. it's the same. When you click on submit button of perform harness, it will also call the same rule(i.e. Activity) 'FinishAssignment'. This activity Validates, Sets the Task status, completes Assignment and checks for back to back assignments then diplays the Review or Perform harness.
"finish assignment" action is not different from default "submit" button. We use "finish assignment" action when we need to process the assignment with out clicking on the default buttons. For ex: when we want to process the assignment on click of a button, we use "finish assignment" action on that link.
In other words, it is OOTB activity available for us to be called from the events like click event from the application specific sections. For the Perform harness, the button is already configured with the same activity. Hope this helps.