I had no idea what a powerful difference this would make. It's remarkable that a child (or an adult for that matter) can learn to mouth the words "I'm sorry" like a memorized line in a stage play without ever engaging his or her heart.
The difference in these two phrases goes beyond the words. The difference is actually a shift from a monologue to a dialogue. I can throw the words out and never know (or care) if the apology is received in the heart-disengaged monologue. If, however, I look the offended person in the eye and ask for forgiveness, I must wait to receive his or her response. And as I have found, it's nearly impossible to "fake" asking for forgiveness.