Difference betwen Integration and Import
Integration means that the events in your external calendars are displayed within your Joomla calendar directly. During synchronization, the database is not touched. For example when you integrate your Google calendars, then a HTTPS call is made to googleapi.com.
On the other hand, when you import the events from your external website through AllEvents Magnet, then it creates the event's in the database of tour favorite events manager component. When you import these events they are stored in the Joomla database. A link is created beween the external event and the internal event, so if you reimport the same event, it's only be updated (no new creation).