They are the same.
“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, the “
kingdom of God” = “
kingdom of Heaven.”