What is the difference between an appeals court and a trial court in the US government?

The difference here is that a trial court is one in which
trials are originally held.  In these courts, there are typically juries that are
listening to the cases and are making determinations of fact.  This is unique to a trial
court.

In an appellate court, trials are not held.  There
are generally not any determinations of fact.  Instead, appeals courts are places where
attorneys appeal the verdicts handed down in trials.  The attorneys must appeal the
verdicts by claiming that the judges in the trials made errors of law.  In other words,
an attorney cannot simply appeal on the basis that their client was innocent and the
jury made a mistake.  Instead, the appeal must be based on the claim that the judge made
a mistaken ruling that hurt the attorney's client.

Overall,
then, trial courts hold trials where findings of fact and law are made.  Appeals courts
hear appeals that claim that findings of law in the trials were
incorrect.