The Edit Task Level, along with the nature of the user-task relationship determines the specific actions the user will/will not be able to perform on the task.
This may best be understood with the chart below. Blue squares in the chart indicate that the task creator can perform the given action. Green squares indicate that a user assigned to the task (as Assigned User or as Reviewer) can perform the given action. Orange squares indicate that a user assigned to the project who is neither the task creator or assigned to the task can perform the given action.