This summary is not the rule. The rule text controls.
Here's a plain-English summary:
This rule covers two different ways a case can end up in arbitration instead of a regular court trial. If the court system has set up a special arbitration program for your type of case, then a specific set of statewide rules (found in Part 28 of the Rules of the Chief Judge) controls how that process works. This is a program the courts create to help move certain cases through arbitration instead of a full trial.
The second part of the rule applies when both sides in a case agree on their own to use arbitration to settle a claim. In that situation, the process follows a different set of rules, found in Article 75 of the CPLR (the state's Civil Practice Law and Rules). This covers things like how the arbitration is run, how a decision gets made, and how that decision can later be enforced or challenged in court.
The main point is that arbitration in NYC Civil Court can happen two ways: through a court-created program or through a private agreement between the parties. Depending on which path applies, different rules control the process from start to finish.