A lien is a claim that can affect the property or the money due at closing. A payoff is the current amount and instructions the lender, creditor, or tax office gives to resolve what is owed. An older bill or letter may not show the amount needed now.
The office or creditor owed confirms the current balance and payoff or release instructions. The title company checks ownership and recorded claims for the transaction and works confirmed amounts into the proposed closing figures.
You don't need to pay off your back taxes before we settle. We buy houses with back taxes and liens — payoffs get handled through the closing, not by you upfront.