Your mother was more interested in teaching you how to respond when you do something you know is wrong, rather than punishment for the sake of punishment. That's significant and important.

When I approach a person I have sinned against, I apologize and take responsibility for what I did, but I never ask for forgiveness because it's not fair to put them on the spot like that just because I did something shitty. Often, people do forgive but they need time to sort things out. I'm not going to put that pressure on them.

I'm going to have to approach some people soon, as I'm on Step 8 in my recovery program and I'm so intimidated!

Taking responsibility and confessing the sin is my work to do, forgiveness is the work of the injured party and I can't do that work for them.

With God, I do ask for forgiveness because God does forgive. I personally make good use of sacramental confession as it's an assurance of God's forgiveness that I can hear, and the priest can help with counsel on amendment.