I've been thinking of this all day and here is my theory.
Acceptance
Someone borrows money from you and says they'll pay you back. They haven't paid you. You accept that they owe you money and may never pay you back. You accept the fact that you can't force them to pay you back.
Forgiveness
You free them from the debt. They no longer owe you the money. They never have to pay you back. They are forgiven the debt.