You ask if the kingdom and the church are the same? Yes they are.
During the personal ministry of Jesus, while he was at Caesarea Philippi with his disciples who were later to become his apostles, he asked them, "Whom do men say that I the son of man am?" Lets look at the whole conversation they had at that time.
Matt.16:13, Now when Jesus came into the district of Caesarea Philippi, He was asking His disciples, ?Who do people say that the Son of Man is??
14 And they said, ?Some say John the Baptist; and others, Elijah; but still others, Jeremiah, or one of the prophets.?
15 He *said to them, ?But who do you say that I am??
16 Simon Peter answered, ?You are the Christ, the Son of the living God.?
17 And Jesus said to him, ?Blessed are you, Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven.
18 I also say to you that you are Peter, and upon this rock I will build My church; and the gates of Hades will not overpower it.
19 I will give you the keys of the kingdom of heaven; and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven.?
In answer to the question that Jesus asked, Peter replied, "Thou are the Christ, the Son of the living God." To this Jesus replied that the Father in heaven had revealed this to him. Jesus then stated, "Upon this rock, (the confession that Peter just made) I will build my church, and the gates of hell shall not over power it, and I will give you the keys of the kingdom of heaven.
Note that here Jesus uses the term church and kingdom interchangably
Mark 9:1 And Jesus was saying to them, ?Truly I say to you, there are some of those who are standing here who will not taste death until they see the kingdom of God after it has come with power.?
Luke 7:27, But I say to you truthfully, there are some of those standing here who will not taste death until they see the kingdom of God.?
Here Jesus plainly states that some of the disciples standing there would not die before they saw the kingdom come, and it would come with power
Luke 24:46. and He said to them, ?Thus it is written, that the Christ would suffer and rise again from the dead the third day,
47 and that repentance for forgiveness of sins would be proclaimed in His name to all the nations, beginning from Jerusalem.
48 You are witnesses of these things.
49 And behold, I am sending forth the promise of My Father upon you; but you are to stay in the city until you are clothed with power from on high.?
Here Jesus said repentance and the forgiveness of sins would be preached beginning at Jerusalem, and that the apostles should stay in Jerusalem until they received power from on high.
Acts 1:4, Gathering them together, He commanded them not to leave Jerusalem, but to wait for what the Father had promised, ?Which,? He said, ?you heard of from Me;
5 for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.?
6 So when they had come together, they were asking Him, saying, ?Lord, is it at this time You are restoring the kingdom to Israel??
7 He said to them, ?It is not for you to know times or epochs which the Father has fixed by His own authority;
8 but you will receive power when the Holy Spirit has come upon you; and you shall be My witnesses both in Jerusalem, and in all Judea and Samaria, and even to the remotest part of the earth.?
Note thus far in these passages Jesus said, "I will build my church, and I will give to you Peter the keys to the kingdom." Matt. 16:18.
Some of the apostles would not die until they saw the kingdom come with power. Mk. 9:1
They were to remain in Jerusalem until they received Power. Luke 24:49
They, the apostles would receive power when the Holy Spirit came upon them. Acts 1:5-8
The Power came when the Holy Spirit came upon them on the day of Pentecost as recorded in Acts 2.
Acts 2:1, When the day of Pentecost had come, they were all together in one place.
2 And suddenly there came from heaven a noise like a violent rushing wind, and it filled the whole house where they were sitting.
3 And there appeared to them tongues as of fire distributing themselves, and they rested on each one of them.
4 And they were all filled with the Holy Spirit and began to speak with other tongues, as the Spirit was giving them utterance.
Beginning in verse 14 Peter begins preaching that the Christ that they had crucified was truly the Son of God, and that God had raised him from the grave and set him at his own right hand, where he was reigning over his kingdom. Not verses 30-36.
Acts 2:30, And so, because he was a prophet and knew that God had sworn to him with an oath to seat one of his descendants on his throne,
31 he looked ahead and spoke of the resurrection of the Christ, that He was neither abandoned to Hades, nor did His flesh suffer decay.
32 This Jesus God raised up again, to which we are all witnesses.
33 Therefore having been exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He has poured forth this which you both see and hear.
34 For it was not David who ascended into heaven, but he himself says: ?The Lord said to my Lord, ?Sit at My right hand,
35 Until I make Your enemies a footstool for Your feet.? ?
36 Therefore let all the house of Israel know for certain that God has made Him both Lord and Christ?this Jesus whom you crucified.?
God had sworn to David that He would raise up one of his descendants to sit on his (Davids) throne.
Psalm 132:11. The Lord has sworn to David A truth from which He will not turn back: ?Of the fruit of your body I will set upon your throne.
12 ?If your sons will keep My covenant And My testimony which I will teach them, Their sons also shall sit upon your throne forever.?
Peter says by the inspiration of the Holy Spirit that this prophesy was referring to Christ, and the God had fulfilled it by raising up Christ to sit at his right hand.
Note again, Peter used the keys to open the doors of the kingdom for the first time. Matt 16:18
The only one of the apostles that had died was Judas. Mark 9:1
The power came with the Holy Spirit which came on the day of Pentecost. Acts 2
The Kingdom came when the power came. Mk 9:1,
Repentance and the remission of was preached in the name of Jesus Christ beginning at Jerusalem.
Those Jews that heard Peters preaching were convicted in their heart and cryed out;
Acts 2:37, Brethren, what shall we do??
38 Peter said to them, ?Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit.
Acts 2:41, So then, those who had received his word were baptized; and that day there were added about three thousand souls.
verse 46, And they, continuing daily with one accord in the temple, and breaking bread from house to house, did eat their meat with gladness and singleness of heart, 47Praising God, and having favour with all the people. And the Lord added to the church daily such as should be saved.
Peter had just finished proving by the prophets that God had raised Christ from the grave to sit on His throne, reigning over his kingdom at the right hand of God the Father. He preached repentance and the remission of sins in the name of Jesus Christ to those Jews.
3000 of them obeyed the gospel and in verse 47 it say they were added to the church, therefore we can see that when the power of the Holy Spirit came, the kingdom came, and when the kingdom came the church came.
Now let us look at it from another perspective.
John 3:1, Now there was a man of the Pharisees, named Nicodemus, a ruler of the Jews;
2 this man came to Jesus by night and said to Him, ?Rabbi, we know that You have come from God as a teacher; for no one can do these signs that You do unless God is with him.?
3 Jesus answered and said to him, ?Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.?
4 Nicodemus *said to Him, ?How can a man be born when he is old? He cannot enter a second time into his mother?s womb and be born, can he??
5 Jesus answered, ?Truly, truly, I say to you, unless one is born of water and the Spirit he cannot enter into the kingdom of God.
Jesus here told Nicodemas that unless one was born again he could not see or enter the kingdom of God. Jesus was here speaking of water baptism as the following verses will show.
Col 1:13, For He rescued us from the domain of darkness, and transferred us to the kingdom of His beloved Son,
14 in whom we have redemption, the forgiveness of sins.
Acts 2:47 says those who had received the remission of sins were added to the church.
Col 1:13 says those christians at Colossee had been translated into the kingdom of His beloved Son where they had redemption which is the same as the forgiveness of sins.
John 3:3-5, Jesus said no one could enter the kingdom until they had been born again, but the colossians were in the kingdom therefore they had been born again, but how?
Paul says in Eph. 1:7, that redemption is in Christ, and Gal. 3:27 says we are baptized into Christ. Therefore when we are baptized into Christ, we receive the forgiveness of sins and are translated into the kingdom which is the same as the church.
Again let us look at what Peter said in 1 Pet 1:22, Since you have in obedience to the truth purified your souls for a sincere love of the brethren, fervently love one another from the heart,
23 for you have been born again not of seed which is perishable but imperishable, that is, through the living and enduring word of God.
Peter here says we purify our souls when we obey the truth, and in doing so we are born again, therefore when we hear the gospel, believe it, repent and are baptized for the remission of sins as Peter told them to do in Acts 2, we are added to the church which is the kingdom, which is the body of Christ, (Col 1:18) and in Christ we have the remission of sins, (Eph. 1:7.
Heb 12:28, Therefore, since we receive a kingdom which cannot be shaken, let us show gratitude, by which we may offer to God an acceptable service with reverence and awe;
Rev 1:9, I, John, your brother and fellow partaker in the tribulation and kingdom and perseverance which are in Jesus, was on the island called Patmos because of the word of God and the testimony of Jesus.
1 Thes 2:12, so that you would walk in a manner worthy of the God who calls you into His own kingdom and glory.
2 Thes 2:14, It was for this He called you through our gospel, that you may gain the glory of our Lord Jesus Christ.
These passages show that the kingdom came into existance when the church did and that those early christians were members of it. They were called into the kingdom the church by the gospel.
1 Cor 15:24, then comes the end, when He hands over the kingdom to the God and Father, when He has abolished all rule and all authority and power.
25 For He must reign until He has put all His enemies under His feet.
26 The last enemy that will be abolished is death.
This passage shows Christ is reigning now and will until all enemies are overcome and the last enemy to be destroyed is death. Then he will deliver the kingdom back to God the Father. When will this take place? At the resurrection when death will be no more.