Then could you explain the functional difference, because (if?) you are correct...I don't see it.
It's not up to me to answer for anyone else, but to me forgiveness shows strength of character when the other person demonstrates two basic principles: repentance, and reform.
They (the offender) are sincerely sorry, they repent (go in the opposite direction), and they reform their behavior so as not to make the same mistake or intentionally do the same wrong again.
If they demonstrate sincerity of repentance and reform, then that shows they are making the effort to learn from their errors and to change their character for the better.
In that case then the onus is upon me to try and demonstrate the patience and forgiveness necessary to allow them to continue to improve their character rather than to perpetually condemn them for their previous errors, or sins, or misdeeds.
But that process is a two way street. The onus is upon me is to forgive the sincere repentant. The onus is upon them to seek to prove that they are indeed sincere by demonstrating a different type or class of behavior.
When both parties meet their obligations then good progress can be made at beneficial and necessary reform.
When neither meets their obligations it is impossible to reform.
If only one meets his or her obligations then it is extremely difficult to reform. Because if the aggrieved party will not forgive the other then it makes it difficult for the offender to ever prove himself worthy, even if he has reformed. No proof will be ever be acknowledged as good enough.
But if the offender only seems to reform or is given forgiveness too easily and without real effort then that only encourages him in his previous misbehavior.
And of course both parties must often allow enough time to pass to test their new condition.
That's my view.
Forgiveness requires obligations on the part of everyone involved.
And demonstrations of sincerity and change.