Saying sorry should be about taking responsibility, having empathy and repairing a relationship.
If an accident has happened, it is enough to say sorry and look after the person who has been hurt. If the conflict is intentional, then the relationship must be repaired by apologizing properly. We do this by saying
I am sorry for …. (this is taking responsibility)
It was wrong because… (this is empathizing with how the behaviour made someone else feel)
Will you forgive me? (this is a chance to repair the relationship)
We will be following this model of apologising in school to help children to develop responsibility, empathy and respectful relationships with each other.