The essential one is dedicated to sessions and is usually named MoodleSession. You must allow your browser to place this cookie in order to maintain continuity of work and keep you logged in while moving between pages. When you log out or close your browser, this cookie is deleted from your browser and from the server.
The second cookie is used purely for convenience and is usually named MOODLEID. It stores your username. This means that when you return to this website, the 'username' field on the login screen will be filled in automatically.
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