Appellate courts have the power to review judgments from lower courts (trial court) or tribunal,(United States Courts) with many only hearing cases on a discretionary basis. Appellate courts do not hear new evidence and only review cases from trial courts.(Wex Dictionary)
Intermediate appellate courts
An intermediate appellate court is one that is between the initial trial court and the court of last resort of the state or federal government. Eight states do not have any intermediate appellate courts, which are Delaware, Maine, Montana, New Hampshire, Rhode Island, South Dakota, Vermont, and Wyoming.(Ballotpedia)
Court of last resort
A court of last resort is any appellate court that does not have a higher court.(34 USC § 10251(a)(16)) On the federal level and in all fifty states, the supreme court is the court of last resort.(Ballotpedia)
Circuit and district courts
District courts are the first level of appeal in a court case on the federal level. Some states name their trial courts circuit or district courts.