To research Wayne’s question further, we find that the term “Kingdom of heaven” is not found at all outside of Matthew, while the phrase “Kingdom of God” is found 48 times in the other gospels. Why indeed would Matthew choose to use a second term, and then use it so often?
Wayne’s question asks if “it is possible” that Matthew’s choice of wording refers to something different and the answer is that of course it is possible.
For many, the Kingdom of heaven refers exclusively to the reign of God in the place of the afterlife, i.e., “heaven” (however, many scholars and theologians believe the Kingdom refers to a spiritual reign that exists both in the here-and-now as well as in the afterlife). When trying to understand the biblical place of the afterlife, we discover that Jesus told one of the thieves being crucified next to him that “Today you will be with me in paradise” (Luke 23.43). Is paradise a synonym for “heaven,” or does it refer to a different place?
Then in 2nd Corinthians Paul writes about being caught up to “the third heaven” (12.2). Could this refer to multiple places as well?
According to some sects of Christianity this is exactly what is meant by the difference between the Kingdom of God, the Kingdom of heaven, paradise, and the third heaven. In one sect, paradise will one day be what the book of the Revelation calls “the new earth” (21.1), a place on earth for those who don’t quite make it into “the new heaven.” In another sect, the third heaven delineates the type and literally the level of heaven one can achieve through right living both here and in the celestial realm. In any event, it is clear that there are those who believe the various “Kingdoms” do indeed have a multiplicity of meanings.
However, orthodox Christianity and most scholars believe otherwise. The traditional understanding of the terms “Kingdom of God: and “Kingdom of heaven” is that they share a like meaning. But why would Matthew use the second term?
The answer is found in Matthew’s intended audience. When Matthew wrote his gospel, he wrote it with a Jewish readership in mind. This is clear not only from the content and style of his writings as a whole, but especially because of his repeated references to Jesus’ fulfillment of Old Testament prophesy, as well as his references to Jewish holidays and customs without explanations (Luke, on the other hand, wrote for a non-Jewish audience and he explains nearly every Jewish custom and holiday for his readers).
A third reason we know Matthew was writing for a Jewish audience is because of his word choice for the Kingdom of God. He chose to use the circumlocution “Kingdom of heaven” in place of the “Kingdom of God.” Why? Because according to Jewish custom it is forbidden to say the name of God. So to refrain from offending his readership, Matthew used the phrase “Kingdom of heaven” rather than the more common expression “Kingdom of God.”
So, is it possible that the Kingdom of God and the Kingdom of heaven are different? Certainly. To limit the possibilities is to assert too much. On the other hand, the evidence seems to indicate that Matthew chose to honor the sensibilities of his readership and so made his word choices carefully.