The phrase “kingdom of Heaven” occurs thirty-two (32) times and only in the Gospel of Matthew. The phrase “kingdom of God” occurs thirty-two (32) times in the Gospel of Luke, the most of any book in the Bible.
An examination of Synoptic parallels will demonstrate that the two phrases refer to the same idea.
“the kingdom of Heaven is at hand” (Matt. 4:17) || “the kingdom of God is at hand” (Mark 1:15)
“Blessed are the poor in spirit, for theirs is the kingdom of Heaven” (Matt. 5:3) || “Blessed are the poor, for yours is the kingdom of God” (Luke 6:20)
“Among those born of women there has not risen a greater than John the Baptist, notwithstanding he who is least in the kingdom of Heaven is greater than him.” (Matt. 11:11) || “Among those born of women there is not a greater prophet than John the Baptist, but he who is least in the kingdom of God is greater than him.” (Luke 7:28)
“the mysteries of the kingdom of heaven” (Matt. 13:11) || “the mysteries of the kingdom of God” (Mark 4:11 cp. Luke 8:10)
“the kingdom of Heaven is like a grain of mustard seed” (Matt 13:31) || “the kingdom of God...is like a grain of mustard seed” (Mark 4:30-31 cp. Luke 13:18-19)
“The kingdom of Heaven is like leaven” (Matt. 13:33) || “the kingdom of God...is like leaven” (Luke 13:20)
“Except you be converted, and become as little children, you shall not enter into the kingdom of Heaven” (Matt. 18:3-4) || “Whosoever shall not receive the kingdom of God as a little child, he shall not enter therein” (Mark 10:15)
“Allow little children, and do not forbid them to come to me, for of such is the kingdom of Heaven.” (Matt. 19:14) || “Allow the little children to come to me, and do not forbid them, for of such is the kingdom of God.” (Mark 10:14 cp. Luke 18:16)
“a rich man shall hardly enter into the kingdom of Heaven” (Matt. 19:23) || “How hardly shall they who have riches enter into the kingdom of God!” (Luke 18:24)
In other words, “kingdom of God” = “kingdom of Heaven.” If this is so, then “God” = “Heaven,” which leads us into my next point.
“Heaven” as a Circumlocution or Substitute for “God”
The reason why Matthew uses the phrase “kingdom of Heaven” more often than “kingdom of God” (which he uses only five (5) times in his gospel, although there are textual variants) is because he wrote to a Jewish audience, and the Jews did not pronounce the Tetragrammaton יַהְוֶה (Yahveh), and sometimes not even the word אֱלֹהִים (elohim). For example, today, Jews do not say אֱלֹהִים (elohim), but rather, אֱלֹקִים (elokim), and certainly never the Tetragrammaton. Rather than pronouncing those, they used “substitutes.” Some of these substitutes include:
Taken from;
https://hermeneutics.stackexchange....-the-kingdom-of-heaven-and-the-kingdom-of-god