Well, all sin is ultimately against God, and He is the one Who forgives us. The priest gives us a penance (prayer, fasting, sacrifices, almsgiving etc) as “medicine” to repair the damage caused by sin, but this penance is light in comparison to the harm our sins have done to the Church (as the body of Christ) and our neighbors. The stain of sin is purged in…purgatory.
I’m not positive about this, so somebody please correct me if this is theologically wrong, but maybe some of God’s justice will take place in purgatory, for unforgiven sins against others (which we were absolved of in confession.)
I imagine that it would be a bad idea to require penitents to confess or say they’re sorry to people they’ve wronged…it would probably lead to a whole lot more sinning, in fact. Some sins should NEVER be revealed to the wronged parties. Some people may not be prepared mentally or spiritually for someone to tell them something they did against them.
In AA, for example, making amends or restitution to people must only be done when it will not harm yourself or others. It’s done that way for a good reason, for to cause more harm would negate the value of confession in the first place.
Sometimes the confessor will ask you if it’s possible to apologize, or in the case of stealing, they will tell you to give back what was stolen. But if doing that will get you in more trouble, such as being fired if you stole from work or arrested if your neighbor is not so forgiving, they will tell you to give the money to the poor or some charity…
But religiously speaking, our sin is between us and God. Socially, it’s up to the individual to determine what, if any, amends should be made–if we made a good confession, our sin is still forgiven.