This summary is not the rule. The rule text controls.
When a criminal case involving an indictment is moving forward, sometimes it needs to be moved from one court to another within the same county. This rule explains how that transfer can happen, but only if the Chief Administrator of the Courts gives permission first.
If a case is in the Supreme Court in a county outside New York City, it can be moved to the County Court in that same county. This can only happen before the person has entered a guilty plea or before the trial has started. Once either of those things happens, the case can no longer be transferred.
The same process works in reverse. If a case is sitting in County Court, it can be moved over to the Supreme Court, as long as that Supreme Court is holding a term in the same county, either currently or at some point coming up.
The main point of this rule is to allow some flexibility in where a case gets handled, based on practical needs like court schedules or caseloads. It does not change the charges or the facts of the case. It only changes which court building and which judge will oversee it, and it can only happen early on, before major steps like a guilty plea or trial have taken place.