One Kingdom
Could the following pairs of passages show that the kingdom of God and the kingdom of heaven are synonymous? Luke 13:28-29 and Matthew 8:11-12; Mark 1:14-15 and Matthew 4:17; Mark 4:30-32 and Matthew 13:31-32.
"Ye shall see Abraham, and Isaac, and Jacob, and all the prophets, in the kingdom of God, and you yourselves thrust out. And they shall come from the east, and from the west, and from the north, and from the south, and shall sit down in the kingdom of God" (Luke 13:28-29); "Many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven. But the children of the kingdom shall be cast out" (Matthew 8:11-12).
"Jesus came into Galilee, preaching the gospel of the kingdom of God, And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel" (Mark 1:14-15); "Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand" (Matthew 4:17).
"Whereunto shall we liken the kingdom of God? or with what comparison shall we compare it? It is like a grain of mustard seed, which, when it is sown in the earth, is less than all the seeds that be in the earth: But when it is sown, it groweth up, and becometh greater than all herbs, and shooteth out great branches; so that the fowls of the air may lodge under the shadow of it" (Mark 4:30-32); "The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field: Which indeed is the least of all seeds: but when it is grown, it is the greatest among herbs, and becometh a tree, so that the birds of the air come and lodge in the branches thereof" (Matthew 13:31-32).
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Millennial Kingdom / Kingdom Of Heaven
I don't believe that the Bible ever refers to two different kingdoms of God, but always refers to a singular "kingdom"; the millennial kingdom is included in the kingdom of heaven.
"In the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever" (Daniel 2:44).
"Many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven" (Matthew 8:11).
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Kingdom Of Christ / Kingdom Of God
I don't believe that God's kingdom is divided into two kingdoms: "If a kingdom be divided against itself, that kingdom cannot stand" (Mark 3:24), but that the kingdom of Christ and the kingdom of the Father are one, for Christ says "I and my Father are one" (John 10:30), and Paul refers to "the kingdom of Christ and of God" (Ephesians 5:5), and Peter refers to "the everlasting kingdom of our Lord and Saviour Jesus Christ" (2 Peter 1:11).
I believe 1 Corinthians 15:24 means that at the end of the millennial aspect of the kingdom, Jesus will deliver everything over to the Father in preparation for the descent of the Father in New Jerusalem to the new earth (Revelation 21:1-3).
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One Throne
I believe Jesus sits in the Father's throne: "I also overcame, and am set down with my Father in his throne" (Revelation 3:21), because he is God the Son: "Unto the Son he saith, Thy throne, O God, is for ever and ever" (Hebrews 1:8). This is why in the eternal state of New Jerusalem there is a single throne called "the throne of God and of the Lamb" (Revelation 22:1, 3).
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Throne Of David
While I believe the earthly throne from which Jesus will rule during the millennium will be the throne of David (Luke 1:32), I don't believe the millennial kingdom will be a separate kingdom from God's kingdom but rather the arrival of God's kingdom on the earth, according to the word: "Our Father which art in heaven, Hallowed be thy name. Thy kingdom come. Thy will be done, as in heaven, so in earth" (Luke 11:2); compare: "I will not drink henceforth of this fruit of the vine, until that day when I drink it new with you in my Father's kingdom" (Matthew 26:29).
I believe the throne of David "shall be established for ever" (2 Samuel 7:16), just as "the throne of God and of the Lamb" are forever (Revelation 22:1, 3).