To give you short tips, by default you have the same organization in Studio and Portal, but they could be different: Studio organization would be for test purposes and Portal one for production purposes. Publishing the organization enables to synchronize Portal organization with the Studio one (only for the local portal (embedded in the Studio), it could not be used for the portal installed on a production server). Exporting/Importing the organization is another option to synchronize organizations between Studio, Portal and to backup it.
With the local portal, you can publish the organization.
With a portal installed on a remote server, you can export it from the Studio and import it from the Portal. The result is the same as publishing, with 2 steps instead of 1.
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