I believe the answer is: State or Federal courts handle most appeals from the state courts of last resort, whereas the state courts address most crimes and civil cases
In the U.S court system, the majority of cases is settled within the local court where the dispute/the violations happened. The federal courts only handle the case if it couldn't be handled at both the local court and the court of appeal.
From an average of 8000 request a year, the supreme court only handles around 1% of them.