http://www.kjvbible.org/thekingdoms.html

Kingdom of God is within born again believers and in the third heaven. Kingdom of heaven is King Jesus ruling in righteousness on earth. Don't let the term "heaven" throw you.

The Gospels with the exception of Matthew use "Kingdom of God'' synonamously with " Kingdom of Heaven" but this is much contended as to why. I believe that as Jesus was present and was God in the flesh, this was true in both cases. He was to fulfill both Kingdoms, but not necessarily at the same time . Solomon and David were imperfect pictures of the "Kingdom of heaven" that Christ will fulfill perfectly in His Millennial reign.

As a rule there is a Kingdom of Heaven(type) from Adam till the cross. Then the Kingdom of God ( within you) from the cross to the Rapture. then the Kingdom of Heaven( repent, do works meet for repentance) program resumes. But this is contended furiously. Hope this helps.