In my opinion, there is no difference between the Kingdom of God and the Kingdom of Heaven; both titles apply to the same Kingdom, for example:
Mat 19:23-24 KJV Then said Jesus unto his disciples, Verily I say unto you, That a rich man shall hardly enter into the kingdom of heaven. 24 And again I say unto you, It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God.
Here in Matthew’s Gospel we find the phrases used synonymously, surely Jesus would have expounded further if there were a need to differentiate between them.
Mar 10:24-25 KJV And the disciples were astonished at his words. But Jesus answereth again, and saith unto them, Children, how hard is it for them that trust in riches to enter into the kingdom of God! 25 It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God.
Mark’s Gospel applied the Kingdom of God on both occasions when he recorded the same conversation.
I have written a Hub on this subject, which goes into more detail.