If you are offered a severance package, it may be a lump sum a certain number of days after signing the agreement, or it may be continued salary payments through regular payroll for an agreed number of weeks or months.
Though there are practical implications for you financially, legally, these are no different. For purposes of unemployment, for example, the key question is not how the money is paid, but whether you signed a release of claims. If you signed a release of claims, you should be able to collect whether it is a lump sum or salary continuation (though be advised that the DUA is sometimes confused by this, and you should be prepared to show them your severance agreement).
The other practical implication is that if you are on salary continuation and your employer wants to claim you have violated some term of the agreement (i.e., non-disparagement), all they have to do is stop making the payments. In contrast, if they have made a lump sum payment, they would have to bring a claim and actually prove the violation in order to recoup the severance payments.