The other part of saying sorry is atonement. That's when you ask the other person's forgiveness. These days when someone says "forgive me" they seem to think that merely saying the words should be enough, but traditionally this request to mend a hole in the relationship requires the person asking for forgivness to actually do something to make amends for whatever they have done.
Sometimes it's obvious. You accidentily put a ball through next-door's window; you expect to replace it. But with less immediately tangible situations people often seem to think that saying the words should be enough. An example occured yesterday when I was playing the online super villain game City of Villains.
Someone had invited me on to a team that was much higher level than my character, but the game has a system where you can 'sidekick' a lower level player and they are boosted to the level of the higher player while teamed up. All was going fine and well, except that my partner became (for reasons irrelevent to this article) fed up and decided to leave. He committed one of the worst breaches of ettiquette possible in an online game by quitting the team during a fight. Apart from any effect it had on the others to lose a team member at this point, it caused me to lose my sidekick status and suddenly I was surrounded by enemies who had just gained 10 levels relative to me and I was face down in the gutter.
I was surprised that he had the gall to contact me after this, but he did, apologizing to me for leaving but he wasn't happy with the team. It wasn't until I pointed out that his action was calculated to kill me that he even considered the effect his action had on anyone else, and he was genuinely upset and asked me to forgive him.
And I thought "What is my forgiveness worth to you? Are you prepared to fix the trouble you caused me? Are you about to help me work off the experience debt I acquired due to your actions? No, you just want me to say the words so you can feel better. Why should I let you off the hook when your action is going to take me maybe a half hour's effort to fix?".
So I said I'd forgive him when I had worked off the debt.
He didn't offer to help.