Although most often called the "Kingdom of God," occasionally other terms
are used in describing the Kingdom. Three of the writers of the Gospels—Mark,
Luke and John—use the term "Kingdom of God" to refer to the Kingdom
by name.
"Kingdom of heaven" is a term used exclusively by Matthew, with 32 references
in his account of Jesus Christ. However, he uses the terms "kingdom of
God" and "kingdom of heaven" interchangeably. In Matthew 19:23,24, he
uses the terms in consecutive verses, clearly implying that they were synonymous.
Often he calls it simply "the Kingdom."
Why did Matthew call it "the kingdom of heaven"? Because heaven is where
God is, as Jesus Christ made plain (Matthew 5:34,45,48). Matthew makes
it clear that the Kingdom was not, at that time, an earthly monarchy like
the kingdoms around them. However, he understood that it was a kingdom
to come, for which Christ's followers are to pray (Matthew 6:10).
The apostle Paul usually refers to it as "the kingdom of God." However,
acknowledging the role of Jesus Christ as the Ruler of that Kingdom and
the way by which we enter that Kingdom, he also calls it "the kingdom of
Christ and God" (Ephesians 5:5). He also expresses the deep, loving relationship
between God the Father and Jesus Christ by calling it "the kingdom of the
Son of His love" (Colossians 1:13).