Without turning this into a criminal procedures lecture, the practical difference surrounds who decides the punishment. When a judge rejects a deal they are as

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.