Q: Is the gospel of salvation beautifully spoken of in Romans 1:16 the same as the gospel of the kingdom spoken of in Matthew 4:23 and other places?
A: I believe it is, but I also believe that the gospel of the kingdom is much more, and not merely limited to “salvation.”
One of the series of three in scripture that I have seen is: (1) salvation (2) sanctification (3) purification. If one matches this with the previous series of three we spoke about:  See the Kingdom (John 3:3),  Enter the Kingdom (John 3:5),  Inherit the Kingdom (1 Cor. 6:9-10; Gal. 5:19-21), we see that the easiest and first level of our kingdom walk involves salvation. The next hardest and second level of our kingdom journey is all about sanctification, i.e. working out our salvation with fear and trembling (Phil. 2:12). The final and most difficult leg of our Kingdom of God quest involves purification where all that is not gold, silver & precious stones built on Christ Jesus in our lives is burnt up in a Baptism of Fire (Matt. 3:11; 1 Cor. 3:11-13; Heb. 12:28-29).
There’s freedom in God’s Kingdom to stay at the seeing His Kingdom from a distance phase. Or we can choose to follow the inner pull of the Holy Spirit where we are lead to move on to know Him and the power of His resurrection by walking in the same manner as Jesus did (1 John 2:2-6) knowing the fellowship of His suffering by being conformed to His death in order to attain to the resurrection from the dead (Phil. 3:10-11):  death,  burial,  resurrection. The cross is so glorious (and I desire to never minimize it or the precious Blood of the Lamb), but Jesus story does not leave Him hanging on the cross, so I encourage all of us to follow Him all the way: salvation, sanctification, purification.
The Strong’s Concordance tells us that the word “gospel” (Greek NT: 2098) is not only the glad tidings of salvation through Christ, but also the sayings, and deeds of Jesus Christ as well as the glad tidings of the kingdom of God soon to be set up, and subsequently also of Jesus the Messiah, the founder of this kingdom.
Basically, I believe that the explanation of the gospel can be simplified into the gospel is the Kingdom(s) of the Word of God – Messiah Yeshua.
~ Robin Main
Copyright March 29, 2019 – Sapphire Throne Ministries – Robin Main
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ART: “Pillar of Light” by Orit Martin