I would first try a PFD with a settlement offer, but since its fresh, prob will have to be a PFD in full. A collection will always be a collection even if it says Paid in full/settled for less than full. Thats why you want to try the PFD.
When you pay an account, either in full or under a setlement agreement for less than the full amount, if the payment is accepted by the party as legal fulfillment of the debt, then there is only one current status code (field code 17 of your credit file) for their reporting. That status code is "paid." There is no current status code for reporting "paid for less than the full amount."
That information is separately reported under field code 19, "Special Comments." It would then clarify that the "paid" status was achieved through a payment for less than the full amount of the debt owed. A current status of "paid" does not mean it was paid in full.
Since FICO does not score payment or nonpayment of a debt, but only events that occured along the way, these are not important to FICO scoring. It makes no FICO scoring difference if it was a PIF or a settlement.
The difference in importance comes about when a prospective creditor does a manual review of a consumer's credit report. The Special Comment "paid for less than the full amount" is something they are apt to pay close attention to. It tells them that you have, in the past, not fully met the total debt you accrued.