I think I get the point now.
Assignment and quiz are two different activities in Moodle. Assignement is a task that the student solves with a editor text entry or a file upload. The teacher has to comment and grade manually. After submision and first grading the teacher can 'reopen' the assignment forthe student to resubmit the answer.
Quiz is typically a set of questions with autmatic grading and feedback. Manual grading and feedback is possible i.e. for essay text questions.
Now about the process:
- Teacher creates an assignment and publishes it in the course with a start date and a due date. He also defines the maximum grades and the type of submission and feedback. The description of the assignments includes all information about the type of assignment and what is expected and how the feedback and grading process will work.
- The students works on the assignment and submit the results,
- The teacher gets a mail information if a student has submit to the assignment. Or: he waits for duedate and goes then to the assignments
- The teacher can see the submissions online, comment and grade online or doenload them and grade offline and upoads comments and grade afterwards,
- The teacher can also notify the student to work on assignment a second time.
- Student will be notified via mail that the teacher has commented or graded the submission.
Now a second round starts.
The process is a little bit different.
If the teacher creates a new quiz s/he defines the settings for the quiz: when, how often, how many time for an attempt, grades etc. In general quiz setting he can define also question behaviour when student sees feedback for questions and general feedback for total quiz result.
Then the teacher creates or selects the questions for the quiz.
By editing a quiz queston the teacher will define question text, answering options, correct/wrong answers, weight of question (by points) and (!) feedback for the question, each single answer or all wrong/correct answers. This feedback is very helpfull for students.
If the quiz is published students will run through the quiz one or several times. Depending on the teachers settings the get immidiate or later feedback for the quiz.
If defined the teacher gets a mail notification about a finished attempt by a student. But in most cases teacher don't want to get masses of notification. If there is a vocabulary quiz on weekly base, the check who has finished, not yet started, succeed or failed the quiz after due date.
Teacher can see the total result forthe quiz and the detailled result for each attempt andthe answers for each question per student.
I think you know this process. And I think it will be generally similar in all LMS systems. Itslearnig uses a different model for notification of teachers.
One point that was not discussed is, what does it mean a teacher closes an assignment. Closing can have different meanings: the grading and feedback process is finished, the activity will be closed and students don't have access, the activity is deleted.