The US has a dual court system because there are state courts and federal courts.
The US has a separate court system whose organization and jurisdiction are derived from the US Constitution
VA has a separate court system derived from the Virginia Constitution.
Courts can have original jurisdiction (hearing a case for the first time) or appellate jurisdiction (ability to hear a case from a lower court... second time hearing a case), OR BOTH.
A criminal case is when someone commits a crime that is against the laws of the state or nation, and a civil case involves a non-criminal matter... such as a dispute over a contract or rent.
A felony crime is when someone commits a serious crime such as robbery or murder, and a misdemeanor crime is when a relatively minor crime is committed.