This summary is not the rule. The rule text controls.
If an appeals court needs to issue some kind of legal paperwork or order during a case, that paperwork should look and work basically the same as what's used in regular trial courts. The appeals court doesn't create a whole new system for this. Instead, it follows the same format already set out in Tennessee's civil or criminal court rules, depending on whether the case is a civil matter or a criminal matter.
The same idea applies to how that paperwork gets delivered and handled. When someone needs to be served with documents from the appeals court, or when paperwork needs to be carried out and returned to the court, the process follows the existing rules from civil or criminal trial courts.
In short, this rule keeps things consistent. People and lawyers who already know how service of process works in trial court don't have to learn a brand new system just because a case has moved to the appeals court. The same basic rules carry over.