“The kingdom of the heavens”-the true rendering-is only named in Matthew. It is a dispensational term; while "the kingdom of God" is a moral thing. In keeping with the gospels you name, you find the terms used. Matthew groups his subjects together dispensational; Luke does so morally; both depart from the historic order to which Mark keeps more than any of the others.
With a Jew, the term "kingdom of the heavens" was familiar. (See Deut. 11:21; Psa. 89:29; Dan. 2:44; 4:26-35, and other scriptures.) It is the "rule of the heavens" owned on earth. It was announced as "at hand," not as come, by John the Baptist (Matt. 3), by the Lord (Matt. 4), and by the twelve (Matt. 10). It is rejected, and in Matt. 12, which ends the gospel to the Jew, the curse of Antichrist is pronounced upon the nation, and a remnant owned who obey His Father's win. Then in Matt. 13, the Lord begins a new action, as a sower, and the kingdom of the heavens takes a new character, which the prophets did not contemplate. It is portrayed as a sphere overrun with evil, and a mingled crop-the "mysteries of the kingdom of the heavens," and instead of the true subjects taking their origin from Abraham, they do so from the Word of God, which Christ sows; others accept the authority of Christ nominally as professors.
In Luke, who is the great moralizer, the term used is "kingdom of God," of which He could say in answer to the inquiry of the Pharisees if it came with observation, that it was "in the midst of you." (Luke 17:21 JND), for God was there in Christ. Of the "kingdom of the heavens" it could only be said it is "at hand." and it did not (and could not) commence until the ascension of Christ. To have come in during His presence, it would have been the kingdom of the earth. His authority and that of the heavens were owned, even before the coming of the Holy Ghost, during the ten days of interval, by the disciples, who waited by His directions for that coming. It will run on in its present, confused state until the Millennium. Hence it begins before the Church is started and ends after the Church is complete.
You get two places where the term gets a moral character from Paul-"The kingdom of God is not meat and drink; but righteousness, and peace, and joy in the Holy Ghost" (Rom. 14:17); "the kingdom of God is not in word, but in power." 1 Cor. 4:20. It is the "exhibition or manifestation of the ruling power of God under any circumstances." A man must be born afresh to "see," or "enter in" to it, in the verity of it (John 3); it is not so in the kingdom of heaven, in which tares and wheat mingle. Souls may profess and submit to God's kingdom as merely profession. Hence, in Luke 13:18, he uses the term kingdom of God where nominal profession is noted in the parable, and where the "kingdom of the heavens" might be used interchangeably. Still, none but the saints would be really of it, as born of God.
When the Millennium comes in, the present, confused state of the kingdom of the heavens will be set aside by the judgment of the living, and it will then be displayed in its verity in a two-fold, heavenly and earthly state of things. The Son of man gathers out of His kingdom-the earthly part of it (see Psa. 8; Heb. 2)-all stumbling blocks and workers of iniquity. Then shall the righteous shine forth as the sun in the kingdom of their Father-the heavenly sphere of it. (See Matt. 13:41-43.) F.G. Patterson