Link to full article containing the clarification:
http://www.aqidah.com/creed/articles/kyvik-the-khilaafah-lasted-for-30-years-then-there-was-kingship.cfm
 

Related Link – Allah’s Promise to the Believers that He would grant them Succession:
http://islamtees.uk/2011/09/18/allahs-promise-to-the-believers-that-he-would-grant-them-succession/