In the two sermons from the Temple Mount and the Mount of Olives Matthew records Jesus using the phrases kingdom of God and the kingdom of Heaven. Most of the time Matthew uses the phrase kingdom of Heaven. Only four times does the kingdom of God show up in Matthew. Contrast that to Mark, Luke, and John that use the phrase kingdom of God. PLEASE this does not signal two different kingdoms but two different audiences. Matthew is directing his Gospel to a Hebrew audience; the others are for a more Greek/Gentile reader.
So, why did Matthew use the kingdom of God at all? A careful look at who Jesus was talking to when Matthew changes terms is very important. Matthew 12:28 (Pharisees), 21: 31, and 43 (Sadducees) or the “rulers” of the people. 19:24 is after the rich young man (ruler) left and Jesus uses both “God and heaven” to address His disciples. (For you to get the most out of this please review the reference websites-they are Jewish.) Heaven is the term of the Pharisees and the people, while God is more of the Sadducees and priests. I believe that Jesus used the different terms to needle the rulers, to cause a reaction. Those two groups held very different opinions on angels, resurrections, and what heaven and hell were like. The Sadducees and the resurrection are mentioned in Acts 23:8, Matthew 22:23, Mark 12:18, Luke 20:27.
References: Messianic thought – https://engediresourcecenter.com/2019/09/04/what-is-the-kingdom-of-heaven/ Traditional Jewish thought- https://www.myjewishlearning.com/article/heaven-and-hell-in-jewish-tradition/
The Sermons – Jesus’ response to the demands from the Sadducees were the parables of the two sons and the rebellious tenants. He used the kingdom of God in both of the explanations. These prophetic rebukes came to pass in 70 A.D. (CE) with the Romans destroying Jerusalem and the Temple. Basically, when the Temple was gone, so were the Sadducees (priest). Note-there is a group of Kohen’s (Levitical priests) still living in North Africa.
For the Seven Woes and the parables on the Mount of Olives Jesus used the kingdom of heaven or the kingdom prepared by the Father, these were to the Pharisees or His disciples. Jesus also talks about earthly kingdoms (24:7) and the message of the gospel of the kingdom going to the whole world. Matthew uses the word kingdom more than any other writer. Luke is second.
Heaven – Matthew’s target audience was Jews. I believe that the Holy Spirit gave him the wisdom to reproduce Jesus’ words the way he did. The Jewish believers would have related more to the Pharisee’s teaching about heaven. The thought of the day was that heaven was divided into three different levels. Looking at what is going on in heaven gives you a clue as to the level they were talking about. Birds fly in the heavens, clouds float in one, and the Father lives in the third. No, this is not how Christians view the idea of heaven. Remember, Paul a Pharisee, talks about a man who went up to the third heaven and got a superior revelation.
Olam Ha-ba (“World to Come”) and Gan Eden (“Garden of Eden”) are and were views of the Jews about the afterlife. So, Jesus talking about heaven carries more of the “Garden of Eden” and the world before Satan stole the rule of the earth from Adam. Come, Lord Jesus!
Chapters 24 and 25 – These contain the sermon/parables about the timing of Jesus’ return, how to be prepared, and what we are to do while He tarries. Chapter 25: 31- 46 carries a definite message that not everyone will make it into Heaven. Like the parable of the Ten Virgins, it is directed at people who sit in churches and do not produce the fruit that the Father wants.