I've been thinking about this more and I have come to the conclusion that I think the Bible discusses two types of forgiveness:
Divine/Moral: Bestowed upon humans by God for sins they commit. This forgiveness is given to humans for the benefit of the individual receiving the forgiveness and is realized inside of the moral/spiritual structure outlined in the scriptures. Scriptural references: Law given to Israel, Acts 3:19, etc.
Human: Bestowed upon humans by other humans for real or imagined wrongs. This forgiveness is given to fellow humans for the benefit of the one doing the forgiving although it may lead to repentance, reconciliation a healed relationship. Scriptural references: Matt 5:39, Matt 18:22, etc.