This summary is not the rule. The rule text controls.
Here's what this rule means in plain terms.
The Surrogate's Court itself cannot issue an execution to collect on a decree or order. An execution is a legal tool used to enforce a court decision, like allowing a sheriff to seize property or garnish wages. This court simply does not have that power directly.
Instead, if you want to enforce a decree or order from this court, you have to take an extra step first. You need to file a transcript of the decree or order with the appropriate office, following the process laid out in Section 603. Once that transcript is filed, the decree or order gets treated the same way as a judgment from the Supreme Court. At that point, it can be enforced through a normal execution, just like any other Supreme Court judgment.
In short, this rule sets up a two step process. First you register the decree properly, then you can use standard enforcement tools to collect what you are owed.