Fed. R. Civ. P Rule 3:  “A civil action is commenced by filing a complaint with the court.”

complaint:

1. The initial pleading that starts a civil action and states the basis for the court’s jurisdiction, the basis for the plaintiff’s claim, and the demand for relief.  In some states (cases), this pleading is called a petition. [1]

1. The initial pleading in a civil action , in which the plaintiff alleges a cause of action and asks that the wrong done to him be remedied by the court. [2]

well-pleaded complaint – (1954) An original or initial pleading that sufficiently sets forth a claim for relief — by including the grounds for the court’s jurisdiction, the basis for the relief claimed, and a demand for judgment — so that’a defendant may draft an answer that is responsive to the issues presented.  *  In federal court, a well-pleaded complaint must raise a controlling issue of federal law, or else the court will not have federal-question jurisdiction over the lawsuit.

short-form complaint – (1911) A simplified, convenient, indorsed complaint typically used by pro se litigants.  *  As contrasted with a formal complaint, a short-form complaint may be used in certain actions normally requiring the use of a formal complaint, but maybe construed as conferring jurisdiction while containing a defect, curable by amendment.