The party that makes the motion is known as the movant. A motion can be written or spoken, as the relevant rules require. Various motions can be made throughout a proceeding, but only after the initial complaint has been filed.
See, e.g.; motion to dismiss, motion for summary judgment, motion for judgment as a matter of law, motion for directed verdict, motion in limine, motion to quash, motion to strike, and motion to suppress.
[Last updated in June of 2023 by the Wex Definitions Team]