In the normal usage of words, the "Kingdom OF Heaven" means a Kingdom OUT OF Heaven. The connotation is that the King and Laws already established in Heaven will be transported to somewhere else and enforced. The Kingdom of God is even more simple. It is the area, domain or sphere were God's Kingship is recognized and His Laws are enforced. If Christ does not return to earth, the King will be missing. Who will enforce His Laws. Thus, without Christ there is no Kingdom. But Matthew starts with Jesus Christ, seed of Abraham and seed of David. Immediately we see His status ON EARTH, for that is the domain of Abraham and David. Abraham is promised the Land of Canaan as an "everlasting possession", and he is promised the "Whole World" in Romans 4:13. Our Lord Jesus, being seed of Abraham, must INHERIT Canaan, and He must INHERIT the whole world. And, as seed of David, He is promised to sit on David's Throne forever. He is thus BOTH, (i) King of Israel, and (ii) King of kings.
The Kingdom of Heaven is pointedly NOT for Israel because they are "earthy", are as the "sand of the sea shore", has a Law written forst in stone and later in their hearts, and will display a "terrestrial glory" in resurrection. Much more, the Church is "of a heavenly calling" (Heb.3:1), is born from ABOVE (Jn.3:3-6 - lit.Gk.), Look to heaven for the coming of their Lord, focus on heavenly things, have their treasure in heaven, have a King who came down from heaven and have "celestial glory" in resurrection.
- The Kingdom of David is for Israel and is in Canaan ON EARTH - Jesus is that King in Jerusalem (Zech.14:16)
- The Kingdom of Heaven - the rules enforced in heaven, is brought TO EARTH by our Lord Jesus and the Church. They rule the cities of the Gentiles (Lk.19:17-19)
- The Kingdom of God is established by Jesus thrashing the Gentiles at Armageddon in a military battle (Dan.2:34-35, 44-46). Since the Gentiles are on earth, Christ will be King of the EARTH