What is the relationship between salvation and confession? The connection between believing on Jesus Christ and publicly confessing His name is that both are perfectly consistent with each other. We confess His name by faith. Confession is not a meritorious deed. Confession is not something that we attach to faith as a requirement or prerequisite for salvation. It is not something that completes salvation. Rather, confession is simply an expression of faith. The baptism of the Ethiopian eunuch illustrates this point quite well (Acts 8:34-39).
Audible confession of Christ's Lordship is evidence of a changed heart, as such will certainly bring about persecution. In context, the Apostle Paul is giving particular emphasis to the simplicity of receiving the righteousness of God. The gospel message is so simple that even children can properly make sense of it. Receiving His forgiveness comes by faith, not by keeping the Law. We are saved because God is gracious. We are to place our trust in the work of His Son Jesus Christ. The object of our faith is Him. The foundation of our hope is Him. And a saving faith comes through the preaching of the gospel (Romans 10:14-17).
Justification before God is by faith alone, apart from the merit of good works. However, faith and works cannot be totally divorced from each other. If we have a heartfelt faith which results in salvation, then it follows that we will also recognize our need for a Savior. That is brought about through the repentance of sin. A faith that reflects trust in God cannot exist apart from repentance. So there can be no salvation apart from confession. All of this is simply inherent characteristics of a saving faith and the fruit of a regenerate heart. These things are inextricably connected. The Apostle Paul is not hereby placing faith and confession in a sequential or chronological fashion, but resorting to parallelism. The Reformation Study Bible has this useful footnote:
"10:9, 10 confess . . . believe . . . believes . . . confesses. In the parallelism of v. 10 Paul reverses the order of verbs in v. 9 and thereby indicates that heart-belief and mouth-confession belong together for justification (“righteousness”) and salvation."