Whether or not you are required to report the settlement savings to the IRS as income depends upon two main factors.
First, the difference must be at least $600, and second, if you can show that you were insolvent at the time of the settlement, tax liability does not apply.
Insolvency requires a showing to the IRS that your total liabilities exceeded your assets, which requires submission of financial statements.
Either paying in full or reaching a settlement for less will mandate that the debt balance be updated to show $0 balance.
The primary difference is that if you settle for less, the creditor (or debt collector, as the case may be) can alternately report a status of paid/settled for less than the full amount.
The addition of the statement that it was paid for less informs others that you have a prior history of not paying the full debt that you have obligated, and is never a favorable comment when reviewed by future creditors.
If you pay in full, the updated status will simply read Paid, with no additional comment that it was paid for less than the full amount of the debt.
You can, however, as part of any settlement negotiation include as a condition that the furnisher agree not to report paid/settled for less, and only report the debt as paid. If they accept, then the credit report will then read the same is if the debt was paid in full.
Thus, you may wish to first offer a pay for not reporting any reference to settled for less.
As for entering into a payment plan, regardless of whether it is for a pay in full or a settlement for less, that raises the additional issue of a reset of the statute of limitations for their initiating civil action. If you thereafter default on that payment plan, it has its own ("new") stattue of limitations, which effectively resets the SOL.
If the debt is at or near the SOL for your state, then agreeing to a payment plan may provide a "new" SOL period that could be a consideration if you ever become in default of that agreement.
