There is a difference between the original motivation to forgive and what forgiveness itself actually is. Oftentimes, people start the forgiveness process to rid themselves of unhealthy anger. If they still go through the forgiveness process by committing to do no harm, try to understand who the other person is, bear the pain, and offer respect and kindness toward the offending other person, then this is actual forgiveness. The initial motivation to forgive can change so that a new motivation is to aid the one who acted unjustly.
For further information on this, you might want to read my essay (click the link below), at Psychology Today, entitled, 8 Reasons to Forgive.