The other gospels I heard about never mentioned Jesus and the cross.
Maybe you are talking about something different....
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I am specifically talking about the shed blood on the cross. If it is different from what you have heard then you have only heard the doctrines of the religious.
Salvation under God's grace is based on what Jesus (GOD) did on the cross. It has every thing to do with Jesus' shed blood on the cross that atoned (paid) for ALL the sins of the world. Salvation is only offered to those that trust (have faith) in what Jesus (GOD) did for man on the cross where He, Himself, atoned for all of man's sins of the flesh. God has always chosen those that have faith in Him. In other words God predestinated that those who believe Him are chosen. belief = faith
The Gospel of the Kingdom was about Jesus coming to setup the promised kingdom of the Jews. The Grace Gospel is about what Jesus did for the whole world. The Grace Gospel is about Jesus paying for the sins of the world. The kingdom Gospel was under the covenants made to the Jews only. It included the law.
No one can be saved under the "kingdom gospel". It was only offered under the covenants God made with the Jews and they rejected it. God never made those covenants with the Gentiles. God has reached out to the Gentiles, and the world, through the grace gospel He gave Paul.
Eph 1:7-9
7 In Him we have redemption through His blood, the forgiveness of sins, according to the riches of His grace
8 which He made to abound toward us in all wisdom and prudence,
9 having made known to us the mystery of His will, according to His good pleasure which He purposed in Himself,
NKJV
I have used standard English words that means what they say.