How does an appellate court differ from a trial court

An Appellate Court is not (usually) the Court of original jurisdiction. So, in many cases you would start at a Federal Trial Court (District Court) and would have a normal trial. If you lost, you could appeal to the Appellate Court, who would review the record (only) from the Trial Court for clear error, bias, etc. A new trial does not occur at the Appellate Level, unless it is a court of original jurisdiction.