I was viewing a televised case, the Judge asks the defendant “have any threats or promises been made to you to deliver this plea” before the defendant delivers their guilty plea as part of a plea bargain. I was wondering, how is a plea bargain/plea agreement exempt from being considered a “promise” as the judge words it?
This is covered by Rules of Federal Criminal Procedure Rule 11, which says that
Before accepting a plea of guilty or nolo contendere, the court must address the defendant personally in open court and determine that the plea is voluntary and did not result from force, threats, or promises (other than promises in a plea agreement).
The judge is not required to include a disclaimer (like "other than the plea deal itself") in interviewing the defendant. By asking the question in an unqualified way, the judge will decide whether there were promises made that are outside the scope of the plea bargain.
Because in the United States, the legal system is designed to handicap the government in criminal trials. Plea Deals happen because it is supposed to be in the best interest of both sides to handle it out of court, but that best interest tends to favor the government's position more than the defendant's position. Specifically, a trial costs money and prosecutors do not have a budget to litigate every crime that crosses their desk (especially at the state level, which is where the bulk of the crimes in the U.S. are handled). The plea bargain is a quid pro quo in that, if the defendant agrees to certain terms, the prosecutor will go easy on them and given them reduced sentences and charge them for lesser crimes than what they were busted for (Almost everyone who does jail time for drug possession charges plead down from "Possession with intent to sell" charges... there are bigger fish to fry than putting a college kid who has a single dime bag he intends for personal use in jail for years after all.).
Because the plea deal is a net win for the prosecutor (a criminal is punished and they save money doing it) they would prefer to have plea deals over going to trial in all cases... which means they would be motivated to corruptly influence the defendant to enter the plea deal.
Even if a deal is made, the judge has to accept it for it to be enforced. Thus, if he suspects the deal was not made in good faith or if one party entered into the deal for reasons other than their own free will, they can not accept the deal. And since plea deals are written and offered by the prosecutor, they are going to be the source of any dirty tricks.
All that said, the question is fairly standard. A judge will ask the defendant the same question no matter what plea he/she enters. It's just not as likely that someone was forced to plea "Not Guilty" against their will.