In the United States, District Courts are the trial courts for federal jurisdiction cases in a particular district area. For example, ND Ohio in case citations refers to the trial court vested with US federal jurisdiction for the Northern district of the state of Ohio.
The appeal courts for District Courts are also grouped geographically. For example, 6th Cir. in case citations refers to the US Court of Appeals for the Sixth Circuit, the federal court with appellate jurisdiction over nine District Courts including ND Ohio.
In total, there are thirteen US Courts of Appeals (11 numbered circuits, a DC circuit and the Federal Circuit, which has subject matter, rather than geographic, jurisdiction, including exclusive jurisdiction for tribunal appeals).
One way of comparing these courts to the Australian system is to imagine District Courts as the trial division of State Supreme Courts when exercising federal jurisdiction, and the Circuit Courts as the State Supreme Court Court of Appeal exercising federal jurisdiction.