David gave a good definition for “The Kingdom of God” in I Chronicles 29:11 God’s kingdom includes both Heaven and Earth. Hence in Genesis 14:19,22 he is the possessor of heaven and earth.
However, “The Kingdom of Heaven” is found in the book of Matthew only and is always a reference to God’s kingdom being established on the earth. Matthew 6:10 “…Thy Kingdom Come … In earth as it is in heaven.” Therefore the Kingdom of heaven only refers to God’s reign on the earth, while the Kingdom of God can refer to either His reign on earth or heaven or both.
In Israel’s program it is always in relation to the earth. For the Body of Christ it refers to the heavens. That is the purpose for the Body of Christ – see Colossians 1:15-18.