Secondly, I do not understand this:

None says

Manually mark a Task as completed. This will close the running process and will change the Task’s status to Completed (Use this function to close and change status of remotely executed tasks). To simply change the Task’s status to completed, use task.close()

None says

Closes the current Task and changes its status to completed. Enables you to manually shutdown the task.
danger: Only call Task.close if you are certain the Task is not needed.

What is the difference? My understanding is, that mark_completed additionally (in contrast to close), kills the current Python process on my local machine. Is that right?