There are two kinds of courts in the US - state and federal. Every state has both state and Federal Courts (FC). This article discusses the main differences between the state and FC systems. Note that "to hear" when talking about courts, means the court listening to and ruling on a case.
The first difference is that FC were established by the U.S. constitution, and are controlled by the fed court system, a part of the US government. State (and the city and county courts within each state) courts were established, and are controlled by each state.
The second difference is the jurisdiction of state and FC. The jurisdiction means the types of cases a court is legally authorized to hear.
State courts have broad jurisdiction. Cases such as theft, traffic violations, broken contracts, common fraud, small claims, and family disputes are usually heard in state courts.
FCs limit themselves to the types of cases listed in the constitution and specifically provided for by Congress. Federal courts hear lawsuits against the United States, federal crimes, cases involving violation of federal laws or the constitution, antitrust, bankruptcy, patent, copyright, most maritime cases, and cases where people are in different states and the amount in controversy exceeds $75,000 (this is called diversity jurisdiction).
In some cases, both state and FCs have jurisdiction. This allows parties to choose whether to go to state or FC.
Robbing a person lands you in state court. Robbing a bank lands you in FC. Selling drugs in one town lands you in state court, driving drugs across state lines lands you in federal court. Hit and run usually lands you in state court, hit and run at a federal park lands you in FC.
A person can go to state or FC to bring a case under the federal law, or both federal and state laws. A state-law-only case can be brought only in state court.
It is very important that one files their lawsuit in the correct jurisdiction. If one finds that they are a defendant in a lawsuit, it is very important to consider jurisdiction. If the lawsuit was filed in the wrong court, it may be possible to get their case dismissed.
For more information, please see the link below: http://articles.directorym.com/Jurisdiction_Federal_Vs_State_Court-a935260.html
For more information regarding the differences between state and FC, please see the link below: http://en.wikipedia.org/wiki/State_court#Civil_cases