A Supreme Court petition is a formal request asking the highest court to review a lower court's decision. It presents legal arguments for why the case merits the Supreme Court's attention, aiming to address legal issues or correct lower court errors.

A patent petition is a formal request submitted to a patent office, seeking review or reconsideration of a patent application or a granted patent. It presents arguments and evidence to support why the patent office should grant the requested review, often addressing issues of patentability.

A federal court appeal is a formal request made to a higher court (such as a U.S. Court of Appeals) to review a decision made by a lower federal court. It outlines legal arguments and reasons why the higher court should overturn or modify the lower court's decision, aiming to address errors in the application of law or interpretation of facts.