The “Kingdom of Heaven” is a phrase only found in the gospel of Matthew. Matthew, possibly originally written in Hebrew, is a very Jewish orientated gospel. The writer, Matthew, had a few idiosyncrasies. One of which is that he used the term “Kingdom of Heaven” and “Kingdom of God”, interchangeably:
Mat 19:23 Then said Jesus unto his disciples, Verily I say unto you, That a rich man shall hardly enter into the kingdom of heaven.
Mat 19:24 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, both terms are used to illustrate the same point. Elsewhere, the terms are used interchangeably in gospel harmonies:
Mat 4:17 From that time Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand.
Mar 1:14 Now after that John was put in prison, Jesus came into Galilee, preaching the gospel of the kingdom of God,
Mar 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
We tend also to attach an undue importance to phrases which occur in such writers; few, if any, writers write with the precision of a legal document, and the inverted pyramids which have been built upon chance phrases of Clement or Justin are monuments of caution which we shall do well to keep before our eyes.