what is the difference between heaven and kingdom of God?

Heaven generally implies the state of being with God in the afterlife.

The Kingdom of God is His reign here and now, on earth in our hearts. It precedes heaven, since it starts now.

While some believe that the Kingdom of God and Kingdom of Heaven are referring to different things, it is clear that both phrases are referring to the same thing. The phrase “kingdom of God” occurs 68 times in 10 different New Testament books, while “kingdom of heaven” occurs only 32 times, and only in the Gospel of Matthew. In response to this, some interpreters have come to the conclusion, with the understanding of the Jewish nature of the Gospel of Matthew, that Matthew was writing concerning the millennial kingdom while the other New Testament authors were referring to the universal kingdom. However, a study of the use of the phrase reveals that this interpretation is in error.

For example, in the story of the rich young ruler in Matthew 19:16-24, Christ uses “kingdom of heaven” to speak of the spiritual kingdom. “Then Jesus said to his disciples, ‘I tell you the truth, it is hard for a rich man to enter the kingdom of heaven’” (v. 23). In the very next verse, Christ proclaims, “Again I tell you, it is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God.” So, in answer to the rich young ruler’s question concerning eternal life (v. 16), Christ uses the phrases “kingdom of God” and “kingdom of heaven” interchangeably.

Mark and Luke used “kingdom of God” where Matthew used “kingdom of heaven” quite frequently. In the same parable, the authors used different words, indicating that the two are referring to the same thing. Compare Matthew 11:11-12 with Luke 7:28; Matthew 13:11 with Mark 4:11 and Luke 8:10; Matthew 13:24 with Mark 4:26; Matthew 13:31 with Mark 4:30 and Luke 13:18; Matthew 13:33 with Luke 13:20; Matthew 18:3 with Mark 10:14 and Luke 18:16; and Matthew 22:2 with Luke 13:29. In each of these instances, Matthew used the phrase “kingdom of heaven” while Mark and/or Luke used “kingdom of God.” Clearly, the two phrases are interchangeable because they refer to the same thing.