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As God and heaven are not the same (Gen. 1:1), so the kingdom of God and the kingdom heaven are not the same.
God is a Spirit (John 4:24) and heaven is a place (John 14:2).
The kingdom of God usually refers to a spiritual kingdom that operates within man (Luke 14:21; Rom. 14:17), but occasionally it is associated with the kingdom on earth (Luke 9:27; Gal. 5:21).
The kingdom of heaven is a literal, physical, earthly kingdom that has been placed under the authority of many.
Both kingdoms will be together in the millennial kingdom of the Lord Jesus Christ (Matt. 6:33; Rev. 11:15).