In Matthew 4:17 Jesus’ message is described as “here comes the kingdom of heaven” while in Mark 1:15 it is described as “here comes the kingdom of God”. What’s the difference? The instructor in that class I took in college said “there is none”. Matthew may have used kingdom of heaven thinking that expressly naming God may have been seen as blasphemy by his target audience.
The kingdom of God is where God is the ruler, which can be here on earth since that is one of the things we pray for in the Lord’s Prayer, and also God is the ruler in heaven. It seems that other Christians, not in Matthew’s target audience, have heard kingdom of heaven and think that is talking about after death, or that the world is about to end.