When a Request for Dismissal of a case is filed with the court, the difference between a Request of Dismissal with Prejudice and one without prejudice has significant meaning.
A Dismissal with prejudice means that the person suing you can’t sue you for the same thing that was originally alleged in their lawsuit that they dismissed with prejudice.
A Dismissal without Prejudice means that the filing party can refile their complaint against you at another time based on the same facts so long as it is within the Statute of Limitation. If they file a lawsuit and it is outside the Statute of Limitation, you can file a motion to dismiss the complaint.
I hope that clears things up.