Forgiveness is a rather complex concept.
For example, reinstating a friend who you have broken away from. It seems to me that there are different types of forgiveness that involve one or both of these 2 concepts to some degree. Our High Holy Day prayer book has forgiveness as one of its central themes. We are told over and over that our God is a forgiving God. This is to be a model for us as well as we review our year of behavior towards others.