Each state court has its own levels of appeal. The court of the first level of appeal is generally called the Court of Appeals, though the name often differs from state to state. The next level of appeal, also the highest level in a state court system, is most of the time called the State Supreme Court. This is usually the court of last resort for most lawsuits, and it should not be confused with the U.S. Supreme Court, which is the ultimate last stop for any legal action.
Furthermore, U.S. federal courts have their own levels of appeal. Thus, an appeal from a federal court decision would be appealed to the U.S. Court of Appeals in its region, and then possibly the U.S. Supreme Court