Is the “Kingdom of Heaven” the same as the “Kingdom of God” ?

Yes they are synonymous terms.

Matthew wrote to the Jews and used the term “Kingdom of Heaven”, because Jews were very hesitant to use the word “God”. Mark wrote to Gentile Romans and used the synonymous term, the Kingdom of God.

In those days John the Baptist came preaching in the wilderness of Judea, “Repent, for the kingdom of heaven is at hand.” Matthew 3:1-2 ESV

Now after John was arrested, Jesus came into Galilee, proclaiming the gospel of God, 15 and saying, “The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel.” Mark 1:14-15 ESV