A request letter made in writing, to the court, to grant certain reliefs, with copies sent “to all parties concerned”, informing them of the time and place of such hearing.
Easy way to remember
It is more like an agenda of a business meeting, which is sent to all parties who need to be present, informing them of the points of discussion / the points upon which the judge will adjudicate at the hearing.
A Notice of Motion is a Notice sent to all the parties to a dispute, informing them that the petitioner seeks relief for the mentioned points and moves the court for the same on a specific day at a specific time. It is a copy of the letter through which the petitioner seeks relief. The petitioner maybe the plaintiff or defendant.
It is usually accompanied by an affidavit by the person making the request / sending the Notice of Motion.