You can appeal small claim court judgment to a state trial court. The trial court will review the case like a new case, because small claim court has no transcript on what went on in the small claim court.
A state court usually have three levels. Trial court, appeal court, and supreme court of that state.
A trial is held at the trial court, which generates a record of the court. This is what people usually see court room on TV.
The parties have right of appeal to the appeal court. The appeal court does not reopen the trial, it examines the trial court record and determine if the trial court made a mistake (alleged by the appellant). If there was mistake, the trial court judgment may be vacated and a new trial is ordered. If there was no mistake, the trial court judgment is upheld.
A losing party at appeal court could appeal to the state superme court. However, the supreme court chooses what case it takes. It is not appeal by right. For example, if the supereme court finds the appeal court ruling might set a bad precedent for other courts, the state supereme court might take the case.
A losing party at the state supreme court might appeal to US supreme court, only when a constitutional or federal law issue is at stake. US supreme court chooses which case to take, there is no appeal by right.
