The expression is found only in Matthew, where it appears about 30 times. It is derived from Dan. 2:44; 4:25, 32. The kingdom of God is also mentioned in Matthew, five times out of 70 occurrences in the NT.
Some regard these two terms as identical because of similarities between them. Both are to be established on the earth, Matt. 3:2; Mark 1:15. Mysteries are associated with both, Matt. 13:11; Luke 8:10. Christ associated the parable of the leaven with both, Matt. 13:33; Luke 13:21.
However, differences between the two make it clear that the terms are not identical. The kingdom of God is entered only by the new birth, John 3:3, 5; not so the kingdom of heaven, Matt. 5:20; 7:21. The kingdom of God is eternal, Dan. 4:2, 3; Heb. 1:8, but not the kingdom which precedes it, 1 Cor 15:24; Rev. 20:6. Only the saved are in the kingdom of God, John 3:3, 5, where they are safe, John 5:24; 10:28, 29, but unsaved persons are found in the kingdom of heaven, out of which they will be cast, Matt 13:41-43, 47-51.
The kingdom of heaven therefore may be regarded as the rule of heaven over the earth by Christ when He establishes His kingdom on earth, while the kingdom of God is His sovereign rule in the universe and in the hearts of His people, Psa. 103:19.
William Evans, The Great Doctrines of the Bible, (Chicago: Bible Institute Colportage Assoc., 1912), WORDsearch CROSS e-book, Under: “Kingdom of Heaven”.