In the GRM, an apology is a recovery component expressed for “anything you did (or didn’t do) that may have hurt someone else.” We don’t need to know that it hurt someone else; if our heart thinks it might have hurt them, we need to apologize.
Giving an apology is taking action based on the verb “to apologize.” Saying “I’m sorry” is not an apology. That’s a feeling. One can feel sorry for something they’ve done, but the “action” has not been taken without apologizing. Within the recovery components exercise, we communicate using “I apologize” versus “I’m sorry” to bring emotional completion.