What is the difference between state courts and federal courts? What are some examples of cases of each one?

Federal courts are established under Article III or the U.S. Constitution to try cases that involve violations of constitutional rights or violations of U.S. laws. For example crimes committed on federal property are tried in federal court, as are crimes that involve abuse of the federal mail or international drug trafficking. Federal courts also have jurisdiction over cases that involve violations of bankruptcy, copyright, patent, and certain maritime laws.
State courts are not established by the U.S. Constitution but by individual states. Local courts are established by cities, counties, and other municipalities. State and local courts do not try cases that involve violations of constitutional rights or federal laws, nor do they try cases that involve other laws relegated to the federal courts (bankruptcy, copyright, patent, and certain maritime laws). Instead, state and local courts try cases that involve violations of state or local laws, such as robberies and traffic violations. They handle criminal cases as well as civil cases, but only if the criminal cases do not violate federal laws.