Federal and state courts have different jurisdictions. Jurisdiction can mean either a geographically defined area that a court resides over, or it can mean the laws or legal authority that a court holds for hearing certain types of cases.
The geographical definition applies more to state courts. For instance, Florida laws on certain activities and charges, such as robbery, drug charges and traffic violations, among others, may be different than other states. Unless the charge affects a federal law or the U.S. Constitution and the crime occurred in Florida, the case would be heard here in Florida or in whatever state the crime or activity took place.
In regards to federal jurisdiction, the second definition would be more appropriate. The case would be heard in a federal court depending on the type of case and the authority it falls under.
a) Cases that involve violations against federal laws or the U.S. Constitution would be federal cases.
b) Cases where the United States is one of the involved parties would be a federal case.
c) Bankruptcy laws are governed under federal jurisdiction, as well as copyright and patent laws, and maritime laws. Therefore, these types of cases are usually heard by a federal court, unless they also involve a state law.
d) When there is a conflict between citizens residing in different states, and a sum of money in excess of $75,000 is involved, these cases can be heard in a federal court.
They fall under a “diversity jurisdiction” because the parties are in different geographical jurisdictions.
Some cases may include both federal or state court jurisdiction. In these cases, parties may be able to decide if they want the case heard in a state or federal court. It is not uncommon to see federal drug crimes or federal sex crime charges. However, crimes that are against a state law only must be heard in a state court and vice versa. A crime that involves a federal law only must be heard in a federal court.
Source: Federal Judicial Center, “What the Federal Courts Do” Aug. 14, 2014