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To understand more about a publisher can do we need to clarify about Access Control Level (ACL). In other words ACL governs the permissions that are associated with the individual User levels. There are seven User Groups/levels within Joomla Four only have access to the Site Front-end: Registered, Author, Editor, and Publisher. There are also three levels with access to the Administrator Back-end: Manager, Administrator, and Super Administrator. In addition to the registered User Groups listed above there is a Public (unregistered) or Guest, level.
So a publisher is a User level with access only to Site Front-end functions, but with permission to publish content on the Site.