When you self-forgive you are struggling to love yourself when you are not feeling lovable because of your actions. You are offering to yourself what you offer to others who have hurt you: a sense that you have inherent worth, despite your actions, that you are more than your actions, that you can and should honor yourself as a person even if you are imperfect, and that you did wrong and need to correct that wrong done to other people.
In self-forgiveness you never (as far as I have ever seen) offend yourself alone. You also offend others and so part of self-forgiveness is to deliberately engage in seeking forgiveness from those others and righting the wrongs (as best you can under the circumstances) that you did toward others. Thus, we have two differences between forgiving others and forgiving the self. In the latter, you seek forgiveness from those hurt by your actions and you strive for justice toward them.