The Kingdom of heaven means the kingdom of God.
Matthew 19:14, But Jesus said, Suffer little children, and forbid them not, to come unto me: for of such is the kingdom of heaven.
Mark 10:14, But when Jesus saw it, he was much displeased, and said unto them, Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God.
The kingdom of God has two parts, an outward and an inward. Matthew was the gospel writer who dealt with the outward and visible kingdom, announcing it is at hand. The king is in the midst and was near to establishing his earthly visible kingdom through his chosen people, Israel. However, the outward physical kingdom that men can see cannot take place until the inward kingdom that no one can see is established and that is inside each individual the citizen of that kingdom.
This had already been proven over 1500 years of Israel's history since Moses led the nation out of Egypt at it's birth. They were given the law of God but could not keep it. It only condemned them and revealed their inability. When Jesus came they were subjugated by the nations of the world. Jesus Christ was the only Jew who could keep the law of God perfectly, and he did. His ability stemmed from the fact that he had the perfect righteousness of God in his physical body from his birth, the Spirit, who was his power to resist sin. Here is what the Bible says of him;
.Joh 1:4 In him was life; and the life was the light of men.
This is the Holy Spirit of God
There is no power in the flesh for the perfect holiness that God demands
This is spoken of John the Baptist:
Joh 1:5 And the light shineth in darkness; and the darkness comprehended it not.
6 There was a man sent from God, whose name was John.
7 The same came for a witness, to bear witness of the Light, that all men through him might believe.
8 He was not that Light, but was sent to bear witness of that Light.
Here is a quote of John the Baptist as he witnessed concerning the light.
Jn 3:31 He that cometh from above is above all: he that is of the earth is earthly, and speaketh of the earth: he that cometh from heaven is above all.
32 And what he hath seen and heard, that he testifieth; and no man receiveth his testimony.
33 He that hath received his testimony hath set to his seal that God is true.
34 For he whom God hath sent speaketh the words of God: for God giveth not the Spirit by measure unto him.
Joh 3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
So here are synonyms in scripture.
1) The Spirit of Christ
2) Righteousness of Christ
3) Eternal life
4) The gift of God
5) The Light
A sinner must understand his condition before God and embrace his promise by faith before he can become a citizen of the future visible kingdom of heaven. It is not possible for this order to be reversed because of the nature of the flesh. This is the reason God is establishing his kingdom from heaven at the end of the Bible, in Re 20, rather than the beginning in Ge 4. Sin had to be dealt with first and sinners must be in the kingdom of God before he can go into the visible kingdom at it's inauguration. All others will have been killed in the great tribulation or will be killed before it begins.
LK 19:11 And as they heard these things, he added and spake a parable, because he was nigh to Jerusalem, and because they thought that the kingdom of God should immediately
appear.
12 He said therefore, A certain nobleman went into a far country to receive for himself a kingdom, and to return.
13 And he called his ten servants, and delivered them ten pounds, and said unto them, Occupy till I come.
14 But his citizens hated him, and sent a message after him, saying,
We will not have this man to reign over us.
15 And it came to pass, that when he was returned, having received the kingdom, then he commanded these servants to be called unto him, to whom he had given the money, that he might know how much every man had gained by trading.
......
26 For I say unto you, That unto every one which hath shall be given; and from him that hath not, even that he hath shall be taken away from him.
27 But those
mine enemies, which would not that I should reign over them, bring hither, and slay them before me.
In this parable, this judgement and slaughter of enemies is before the execution of the visible kingdom when personal righteousness is a requirement to enter it.