In an appeal, an appellate court reviews the record of the pre-trial and trial proceedings for legal errors. The record includes the court file, the court reporter's transcript and the evidence and exhibits introduced in the trial court. In general, an appellate court does not consider information that is not contained in the record.
A post-conviction petition is the general name for what is called a "collateral attack" on a conviction. In federal court, they are called habeas corpus petitions. By using a post-conviction petition, a defendant generally can bring evidence before the reviewing court that was not part of the record on appeal, and in this way raise issues that would otherwise not be reviewed.