Well, have a read at this:
https://www.gotquestions.org/kingdom-heaven-God.html
They are used synonymously. However I am familiar with the argument that the Kingdom of Heaven is different because it says that that kingdom is taken by force. But just read the article, it lists the verses that say the same thing but just use the word Kingdom of God in one and Kingdom of Heaven in another. Example:
Mark 4:30-31 "And he said, Whereunto shall we liken the
kingdom of God? or with what comparison shall we compare it? Another parable put he forth unto them, saying, The
kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field:"
Luke 13:18-19 "Then said he, Unto what is the
kingdom of God like? and whereunto shall I resemble it? Another parable put he forth unto them, saying, The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field: "
Matthew 13:31 "Another parable put he forth unto them, saying,
The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field:"
Once you read the context, its the same parable in question.