"Kingdom of heaven" is a term used exclusively in the Gospel of Matthew. The apostle Matthew used "kingdom of heaven" 32 times in his account about Jesus Christ's life and teachings. However, Matthew uses the terms "kingdom of heaven" and "kingdom of God" interchangeably. In Matthew 19:23-24 Matthew 19:23-24  Then said Jesus to his disciples, Truly I say to you, That a rich man shall hardly enter into the kingdom of heaven.
 And again I say to 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.
American King James Version×he uses the terms together in consecutive verses, clearly implying that they were synonymous. Often he calls it simply "the kingdom" (Matthew 6:13 Matthew 6:13And lead us not into temptation, but deliver us from evil: For your is the kingdom, and the power, and the glory, for ever. Amen.
American King James Version×; Matthew 8:12; Matthew 13:19 Matthew 13:19When any one hears the word of the kingdom, and understands it not, then comes the wicked one, and catches away that which was sown in his heart. This is he which received seed by the way side.
American King James Version×, Matthew 13:38 Matthew 13:38The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one;
American King James Version×; Matthew 24:14 Matthew 24:14And this gospel of the kingdom shall be preached in all the world for a witness to all nations; and then shall the end come.
American King James Version×; etc.)
Comparing passages like Matthew 5:3 Matthew 5:3Blessed are the poor in spirit: for theirs is the kingdom of heaven.
American King James Version×and Luke 6:20 Luke 6:20And he lifted up his eyes on his disciples, and said, Blessed be you poor: for yours is the kingdom of God.
American King James Version×shows that the terms meant the same thing:
"Blessed are you poor, for yours is the kingdom of God" (Luke 6:20 Luke 6:20And he lifted up his eyes on his disciples, and said, Blessed be you poor: for yours is the kingdom of God.
American King James Version×).
Why did Matthew use the term "kingdom of heaven"? The Wycliffe Bible Dictionary explains that Matthew "was a Jew writing to his own race and respected their custom of using the name of God as little as possible and therefore spoke of the kingdom of heaven" ("Kingdom of God, Kingdom of Heaven," 1998).
The New Bible Dictionary agrees. "The use of 'kingdom of heaven' in Matthew is certainly due to the tendency in Judaism to avoid the direct use of the name of God. In any case no distinction in sense is to be assumed between the two expressions" (Second Edition, "Kingdom of God, Kingdom of Heaven," 1982).