Prosecutors are not supposed to drop the ball intentionally if the judge rejects the deal. They are supposed to work the case.

Practically, their career would be affected by it too.

There are nuances between jurisdictions, but while a US judge can reject a plea deal they generally cannot reject a guilty plea. A judge cannot force a trial between parties that don't want one. And a trial isn't really possible where the parties agree the facts. The judge can certainly impose a sentence different than that which was agreed between the parties, but any such punishment would have to be based on the agreed facts/charges/pleadings. If the prosecution decides to only charge a lesser offense, the judge's power would be limited to the maximum penalty associated with those reduced charges.

Right. And prosecutions aren't between the victim and the offender. Prosecutions are between The People and the offender. Regardless of how the offender harmed the victim, it's The State that is seeking justice in the matter.

Now, criminal prosecutions take into account the thoughts and feelings of the complainant, but they're not usually bound by them.

Hunter Biden’s guilty plea got rejected.

No. His plea deal was rejected. That is not the same thing.

Right. Plea deals are "I'll plead guilty and save you the trial in exchange for this sentence."

Depending on the court, plea deals can be a horrible gamble by a defendant. Generally you have to enter your guilty plea first, and then the judge decides if they want to let you have that sweet, sweet sentence the prosecution offered.

I know someone who went to court having been offered a plea deal for probation and got 80 years instead when the judge rejected it and sentenced them.

Yeah, this shocked me when I learned it. The actual "deal" is the defendant agrees to plea guilty in exchange for the prosecution giving a specific recommendation of sentence. (In most cases, there are some exceptions of course)

What's the difference (in practice)?

Boeing isn't pleading guilty on its own - it's also agreed to damages.

I agree that a defendant pleading guilty on their own (and throwing themselves on the mercy of the court) would be hard to reject. That isn't what's happened here - the prosecution has, presumably, agreed to the damages, so this is a plea deal, right?

Without turning this into a criminal procedures lecture, the practical difference surrounds who decides the punishment. When a judge rejects a deal they are asserting control over punishment. But a prosecutor can fight back by dropping charges, or reducing to lesser-but-included charges [insert lecture re elements] which would place a cap on the max punishment the judge could adopt. It is a back-and-forth fight between the prosecutor and the judge about who decides punishment, who represents the wishes of the people.

People committed the crimes but Boeing is making the deal, which we haven't seen. I don't understand how "a company" can plead guilty to a crime but shield individuals?

Can I form an LLP before I rob a bank?