Healing a break in your relationship, takes forgiveness plus willingness on the art of your partner to forgive.
Saying “I’m sorry” is just not enough. It is about you and does not communicate to your partner what, if anything, you are or may be sorry about. “I’m sorry” stands alone.
Saying, “I apologize for (what I did)” is not sufficient, either. Your apologetic statement is still about you and stands alone. “Please forgive me (for what I did)” by itself will not offer much towards repairing the breakdown in your relationship.
However, adding, “Please forgive me (for what I did)” is far and away more powerful. “Please forgive me (for what I did)” offers an opportunity to heal the break between you.
With forgiveness and a bit of generosity the two of you just might be able to move on with your lives together.