Reaffirmation" of a debt discharged in bankruptcy means that the debtor who has been "discharged" in bankruptcy from the obligation to pay a debt enters into an agreement to pay it anyway.
"Voluntary repayment" of a debt means that a discharged debtor simply makes payments on a discharged debt without taking on any ongoing binding obligation to pay.
Reaffirmation agreements covering debts discharged in bankruptcy are frowned upon in the Bankruptcy Code. There are strict requirements for such agreements, in order to avoid creditor abuse.
For example, a reaffirmation agreement must be made before the bankruptcy discharge has been granted, and must include a statement indicating that the debtor can rescind the agreement within a period of time after filing it. If an attorney represents the debtor, the reaffirmation agreement must be filed in the Bankruptcy Court with an attorney affidavit stating that the agreement is voluntary and doesn't impose an undue hardship on the debtor or the debtor's dependents. If an attorney doesn't represent the debtor, the Bankruptcy Court must review and approve the reaffirmation agreement.
Even if you don't have a formal binding reaffirmation agreement, though, you're always free to voluntarily make payments on a discharged debt without being obligated to continue payments.
Cathy Moran is a business and bankruptcy lawyer in the San Francisco Bay Area, and was one of the first bankruptcy specialists certified by the California State Bar. Her Web site Bankruptcy in Brief includes much information on bankruptcy.
http://bankruptcy.lawyers.com/Reaffirmation-and-Voluntary-Repayment-of-Debts.html
