A court trial involves the presenting of evidence and witnesses so that guilt or innocence may be ascertained by a jury and/or a judge. In an appellate court, however, an earlier ruling from a trial is being appealed.
In order to do this, the appeal must have grounds, which means the verdict is challenged on the basis that in some way, shape or form, it was not reached in a legal manner and should be overturned. Perhaps the legal counsel was not available or was incompetent, perhaps the evidence was handled improperly, perhaps the jury has been tampered with, etc., and so therefore, an appeal is filed to either void the conviction or to void it and order a new trial be held.
So the appellate cases are unrepresentative of trial cases because the trial has been decided upon, the evidence has been presented and ruled upon, and now the process itself is what is being challenged.
As a general rule, trial courts are triers of fact. That means the trial establishes factually what happened in the case. Appeals courts address and resolve questions or disputes on the law based on the facts established at trial.