All I can say is it is not State Courts (Sorry GradPoint users)
State courts hear far more cases than federal courts.
Federal Appeals Courts
All federal courts hear cases on appeal or original jurisdiction cases.
Federal district courts have trial jurisdiction over most cases in the federal system.
Yes. When both state and federal courts have authority to hear the same case, it's called concurrent jurisdiction.
The state courts hear more cases (by far) than the federal courts.
US Special Courts or courts of special jurisdiction hear a variety of cases, each related to a particular subject matter. For example, US Bankruptcy Courts hear bankruptcy cases; US Tax Court hears federal tax cases; the US Court of Federal Claims hears cases involving monetary damages against the US government; the US Court of Appeals for Veteran's Claims hears appeals of decisions made by the Board of Veteran's Appeals, and so on. Military courts are also considered special courts.
The US Court of Appeals Circuit Courts hear most of the appeals from "lower courts" in the federal court system. The US Supreme Court has the highest federal appellate jurisdiction, and typically hears appeals from the Circuit Courts, although it sometimes hears cases on direct appeal from the US District Courts. Both of these would be considered "lower courts."
The Supreme Court hears three kinds of cases. Cases appealed from lower federal courts account for two-thirds of the cases they hear. They also hear cases appealed from state's supreme courts, and sometimes hear cases that have not been previously heard by a lower court, such as between one state's government and another.
The State Circuit Courts. In the federal system, the US District Courts.
Yes. The State judicial system is similar to the federal judicial system, in that it provides trial courts, intermediate appellate courts, and a state supreme court (or equivalent). Cases initiated in state courts may be appealed in state courts; and some cases initiated in the state courts may eventually be heard in the federal courts.
All courts.