It’s important to understand that whenever the expressions “kingdom of God” and “kingdom of heaven” occur, they must be taken within the context of the passages in which they are found. These expressions can possess several meanings. They can mean the entire creation ultimately under God’s control or the kingdom of Jesus Christ that will come into being when Jesus physically returns to reign. They also can refer to the kingdom of God already present in the hearts and actions of believers who acknowledge Jesus Christ as King.
But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, to an innumerable company of angels, to the general assembly and church of the firstborn who are registered in heaven, to God, the Judge of all, to the spirits of just men made perfect, to Jesus the Mediator of the new covenant, and to the blood of sprinkling that speaks better things than that of Abel (Hebrews 12:22-24 NKJV).
For all practical purposes, the terms “kingdom of God” and “kingdom of heaven” have the same meaning. The New Bible Dictionary describes the use of these two terms in the Gospels:
The kingdom of heaven or the kingdom of God is the central theme of Jesus’ preaching, according to the Synoptic Gospels. While Matthew, who addresses himself to the Jews, speaks for the most part of the “kingdom of God,” which has the same meaning as the “kingdom of heaven,” but was more intelligible to non-Jews. The use of “kingdom of heaven” in Matthew is certainly due to the tendency in Judaism to avoid the direct use of the name of God. In any case, no distinction in sense is to be assumed between the two expressions (ct., e.g., Matthew 5:3 with Luke 6:20) (p. 656).
Although some Bible students in earlier generations expended a great deal of time and energy seeking to establish a difference between these two terms, most authorities today believe that when all of the evidence is examined the two expressions are used in a completely interchangeable way.