When Social Experience communities are disabled, customers can log out of the external site or the customer portal.
Logging out of the external site works normally: After customers log out from the external site, the customer portal logout page is invoked, clearing cookies and logging out the customer, who is redirected to the page specified in the PTA_EXTERNAL_POST_LOGOUT_URL configuration setting. This setting must contain the fully qualified URL of the page you want to redirect customers to.
When communities are disabled and customers click the Logout link on the customer portal, they are logged out of the customer portal and redirected to the page defined by the PTA_EXTERNAL_LOGOUT_SCRIPT_URL configuration setting. This page is the page that logs customers out of the external site, and you can pass a source page parameter to send customers back to the page they were on when they logged out. You also can send them to any other page.