Q. Are the kingdom of heaven and the kingdom of God the same thing?
Yes, they are. Matthew uses the term “heaven” in his gospel because, as an observant Jew, he was as careful as possible not to say the name “God,” in order not to break the third of the Ten Commandments, “You shall not misuse the name of the Lord your God.” Matthew was writing for his fellow Jews, and he was being respectful of their sensitivities as well.
By contrast, Luke was a Gentile writing for a Greek audience, and while Mark was Jewish, he had Roman citizenship and was writing for a Roman audience. So in their gospels, they say “God” where Matthew says “heaven.” Here are some examples.
From that time on Jesus began to preach, “Repent, for the kingdom of heaven has come near.” (Matthew 4:17)
“The time has come,” he said. “The kingdom of God has come near. Repent and believe the good news!” (Mark 1:15)
He told them another parable: “The kingdom of heaven is like a mustard seed, which a man took and planted in his field. (Matthew 13:31)
Then Jesus asked, “What is the kingdom of God like? What shall I compare it to? It is like a mustard seed, which a man took and planted in his garden. (Luke 13:18–19)
John was also writing for a broad audience, and he says “God” rather than “heaven” in the one place in his gospel where the expression occurs, where Jesus tells Nicodemus, “Very truly I tell you, no one can see the kingdom of God unless they are born again” (John 3:3).
So wherever you see the expression “the kingdom of heaven” in the gospel of Matthew, it means the same thing as “the kingdom of God” in the other gospels.
Good Question 