Local government in the Philippines
Local governments have two branches: executive and legislative. All courts in the Philippines are under the Supreme Court of the Philippines and therefore there are no local-government controlled judicial branches. Nor do local governments have any prosecutors or public defenders, as those are under the jurisdiction of the national government.
Federal government of the United States
The district courts are the trial courts wherein cases that are considered under the Judicial Code (Title 28, United States Code) consistent with the jurisdictional precepts of "federal question jurisdiction" and "diversity jurisdiction" and "pendent jurisdiction" can be filed and decided. The district courts can also hear cases under "removal jurisdiction", wherein a case brought in State court meets the requirements for diversity jurisdiction, and one party litigant chooses to "remove" the case from state court to federal court.