Scripture occasionally calls the gospel by names other than "the gospel of the kingdom of God." For instance, the Bible speaks of "the gospel of Christ" and "the gospel of God" (Romans 1:1-16 Romans 1:1-16  Paul, a servant of Jesus Christ, called to be an apostle, separated to the gospel of God,
 (Which he had promised before by his prophets in the holy scriptures,)
 Concerning his Son Jesus Christ our Lord, which was made of the seed of David according to the flesh;
 And declared to be the Son of God with power, according to the spirit of holiness, by the resurrection from the dead:
 By whom we have received grace and apostleship, for obedience to the faith among all nations, for his name:
 Among whom are you also the called of Jesus Christ:
 To all that be in Rome, beloved of God, called to be saints: Grace to you and peace from God our Father, and the Lord Jesus Christ.
 First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world.
 For God is my witness, whom I serve with my spirit in the gospel of his Son, that without ceasing I make mention of you always in my prayers;
 Making request, if by any means now at length I might have a prosperous journey by the will of God to come to you.
 For I long to see you, that I may impart to you some spiritual gift, to the end you may be established;
 That is, that I may be comforted together with you by the mutual faith both of you and me.
 Now I would not have you ignorant, brothers, that oftentimes I purposed to come to you, (but was let till now,) that I might have some fruit among you also, even as among other Gentiles.
 I am debtor both to the Greeks, and to the Barbarians; both to the wise, and to the unwise.
 So, as much as in me is, I am ready to preach the gospel to you that are at Rome also.
 For I am not ashamed of the gospel of Christ: for it is the power of God to salvation to every one that believes; to the Jew first, and also to the Greek.
American King James Version×).
The term "gospel of God" simply shows it originated with God. God delivered the message to earth through His servants. Peter tells us the gospel was sent from God through Jesus Christ. Notice Acts 10:36-37 Acts 10:36-37  The word which God sent to the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:)
 That word, I say, you know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached;
American King James Version×: "The word which God sent to the children of Israel, preaching peace through Jesus Christ–He is Lord of all–that word you know, which was proclaimed throughout all Judea, and began from Galilee after the baptism which John preached ..."
The gospel of God is God's good news about the Kingdom of God. The gospel of Jesus Christ is the good news Jesus brought as God's messenger. All are the same gospel; all are part of the wonderful news of what God has in store for humanity. In a similar manner, Paul sometimes used the term "my gospel" (Romans 2:16 Romans 2:16In the day when God shall judge the secrets of men by Jesus Christ according to my gospel.
American King James Version×; Romans 16:25 Romans 16:25Now to him that is of power to establish you according to my gospel, and the preaching of Jesus Christ, according to the revelation of the mystery, which was kept secret since the world began,
American King James Version×; 2 Timothy 2:8 2 Timothy 2:8Remember that Jesus Christ of the seed of David was raised from the dead according to my gospel:
American King James Version×). This does not mean the message originated with Paul, nor was it a gospel about Paul. It was a message he received directly from Jesus Christ. "... The gospel which was preached by me ... came through the revelation of Jesus Christ," he said (Galatians 1:11-12 Galatians 1:11-12  But I certify you, brothers, that the gospel which was preached of me is not after man.  For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
American King James Version×). Paul's use of the term "my gospel" is proper because he was the one who proclaimed it.
The good news is also called "the gospel of the grace of God" (Acts 20:24 Acts 20:24But none of these things move me, neither count I my life dear to myself, so that I might finish my course with joy, and the ministry, which I have received of the Lord Jesus, to testify the gospel of the grace of God.
American King James Version×). From the beginning we are called by grace, justified by grace and saved by grace (Galatians 1:6-15 Galatians 1:6-15  I marvel that you are so soon removed from him that called you into the grace of Christ to another gospel:  Which is not another; but there be some that trouble you, and would pervert the gospel of Christ.  But though we, or an angel from heaven, preach any other gospel to you than that which we have preached to you, let him be accursed.  As we said before, so say I now again, if any man preach any other gospel to you than that you have received, let him be accursed.  For do I now persuade men, or God? or do I seek to please men? for if I yet pleased men, I should not be the servant of Christ.  But I certify you, brothers, that the gospel which was preached of me is not after man.  For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.  For you have heard of my conversation in time past in the Jews' religion, how that beyond measure I persecuted the church of God, and wasted it:  And profited in the Jews' religion above many my equals in my own nation, being more exceedingly zealous of the traditions of my fathers.  But when it pleased God, who separated me from my mother's womb, and called me by his grace,
American King James Version×; Romans 3:24 Romans 3:24Being justified freely by his grace through the redemption that is in Christ Jesus:
American King James Version×; Ephesians 2:8 Ephesians 2:8For by grace are you saved through faith; and that not of yourselves: it is the gift of God:
American King James Version×). The "gospel of grace" is another appropriate term that focuses on a different aspect of the same gospel Jesus preached: God's enormous love for us, expressed by His grace toward mankind. This message is also called "the gospel of your salvation" (Ephesians 1:13 Ephesians 1:13In whom you also trusted, after that you heard the word of truth, the gospel of your salvation: in whom also after that you believed, you were sealed with that holy Spirit of promise,
American King James Version×). Since our entrance into the Kingdom of God is synonymous with our salvation, there is no conflict in these terms for the gospel. Each complements and strengthens the other.
"The gospel of peace" is also used to describe the good news (Romans 10:15 Romans 10:15And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
American King James Version×; Ephesians 6:15 Ephesians 6:15And your feet shod with the preparation of the gospel of peace;
American King James Version×). The Kingdom of God will bring peace to the earth—an important result of our believing in and acting on the gospel of the Kingdom. Prophesying of God's Kingdom, Isaiah said, "Of the increase of His government and peace there will be no end" (Isaiah 9:7 Isaiah 9:7Of the increase of his government and peace there shall be no end, on the throne of David, and on his kingdom, to order it, and to establish it with judgment and with justice from now on even for ever. The zeal of the LORD of hosts will perform this.
American King James Version×).
All these terms describe the same gospel. They simply emphasize different aspects of the same wonderful message. Jesus Christ came preaching the gospel of the Kingdom of God (Mark 1:14-15 Mark 1:14-15  Now after that John was put in prison, Jesus came into Galilee, preaching the gospel of the kingdom of God,
 And saying, The time is fulfilled, and the kingdom of God is at hand: repent you, and believe the gospel.
American King James Version×), taught His disciples to preach the same message (Matthew 10:7 Matthew 10:7And as you go, preach, saying, The kingdom of heaven is at hand.
American King James Version×) and continued to preach it when He appeared to the disciples after His crucifixion (Acts 1:3 Acts 1:3To whom also he showed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God:
American King James Version×). After Jesus rose from the dead, the apostles preached the same gospel, but with the added understanding of the meaning of Christ's sacrifice and resurrection. Although the terms that describe it may vary, the message is always the same.
The glorious truth is that this whole magnificent message is one seamless gospel, and "it is the power of God to salvation for everyone who believes ..." (Romans 1:16 Romans 1:16For I am not ashamed of the gospel of Christ: for it is the power of God to salvation to every one that believes; to the Jew first, and also to the Greek.
American King James Version×).