If you archive a test, it no longer shows up on your Dashboard. You usually archive a test if you have created a test for demo purposes, or if it is an old test that you no longer need. It will then show up in the Archived Tests section and your homepage won't look as cluttered.
Deleting a Test means removing it from your account. Only Archived Tests can be deleted. You can use the Delete Test feature to clear old tests from your Dashboard that are no longer required.
Note that deleting a Test will neither delete the user's answers, nor the proctoring records. For example, if you load the Google Forms add-on after you delete the test, the test will re-appear on your dashboard, with the old results intact.
If a test has multiple collaborators, the test will not be deleted from the other accounts.