I think perhaps it could be helpful to consider it in this way: We cannot see the forgiveness of sins, but we can see (1) signs of it and (2) the result of it.
(1) We see God's grace, that is, His promise of forgiveness of sins won for us by the person and works of Jesus, tangibly in God's gifts of Baptism and the Eucharist. And I think a case can also be made for Absolution. (This same forgiveness of sins is also found in His Word and by means of the Lord's Prayer or prayer for forgiveness of sins to Jesus in general. It may be confusing, but it's the same Gospel only given to us in different ways for our benefit.)
(2) The result of God's grace, in talking about Sanctification, I think can be summed up as consoled consciences, faith, and good works.
To make this a bit clearer, there's a practical difference between the Roman Catholic system and the Lutheran system in how we understand the Sacraments in light of repentance. In the Roman Catholic system, repentance consists of three parts: Sorrow over sins, a change of heart, and payment for sins through good works. In the Lutheran system, however, repentance consists of two parts: Sorrow over sins, and trust in Jesus.
So, in other words, the Sacraments play a somewhat different role in the Roman Catholic system. They infuse grace to sort of energise the believer to do good. Whereas in the Lutheran system, the Sacraments are means of grace proper. That is, they are God's gifts to us in order to console our contrite hearts, and the effect of this is dependence on God and clear consciences.
Simply speaking, when a person is called to repent and to receive the Eucharist in the Lutheran Church, there is no room for doubt. We know that we cannot pay for our own sins or somehow collaborate with Jesus to pay for our sins. Christ paid for our sins in full upon the cross, and His Words and promise are true, and we trust in that. In the Roman Catholic system, there is a lot of uncertainty. Did I remember to numerate all of my sins? Did I forget any? Did I manage to say the correct amount of Hail Marys and was I sincere enough? In the Roman Catholic system, this is not understood to be a problem, because doubt is seen as a virtue. But in the Lutheran system, we hold that Christ wishes us to know that we are saved. To express this idea with Biblical terms, Paul says to the Ephesians "by grace you have been saved" and not "by grace your original sins were paid and now you have to collaborate with God to pay for your actual sins", nor "by grace salvation may become possible", nor "by grace and your own works you may eventually be saved".
So in summary, the difference that we can discern visibly, is how the Roman Catholic system produces troubled consciences or at least give room for doubt, but the Lutheran system, properly understood, produces clear consciences. Basically, how the Sacrament works and functions in the Lutheran system is that they are God's good gifts to us, and we trust in God's promise contained in those gifts. So the practical difference is this: If we ask “Am I forgiven?” Lutherans can answer: Yes because Christ died for me. Roman Catholics may say the same, but with an asterisk of uncertainty.
