Forgiveness deals with our guilty conscience as well as with the consequences of our sins. Reconciliation leaves no doubt that the forgiveness is personal. Sin violates God’s standards, and those who ignore or disobey His law are not merely law-breakers but enemies.
The gospel reconciles us to God. Because Israel rejected Jesus the gospel went to the Gentiles for “the reconciliation of the world” (Romans 11:15). Remember back to earlier in the letter.
For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life. More than that, we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation. (Romans 5:10–11 ESV)
The relationship was broken, the Lord Jesus restores, reconnects, reestablishes us in peace with the Father. We are being saved by His life for life. It is a life of rejoicing.
To the Corinthians Paul clarified that
The old has passed away; behold, the new has come. All this is from God, who through Christ reconciled us to himself and gave us the ministry of reconciliation; (2 Corinthians 5:17–18 ESV)
Paul magnified his ministry, glorified his reconciling efforts. All of it is from God who has made us new creations in Christ. Our communion with the Lord and with His body is life from the dead.