In a deferred prosecution, no conviction ever enters and the Defendant does not give up their right to a jury trial. They never have to admit guilt. The prosecution of the case is deferred for a specified amount of time and if the Defendant does what they are supposed to do (often classes) and doesn’t do anything they’re not supposed to do (have another offense, etc.) then the case is dismissed with no plea having ever entered.
A deferred judgment requires a guilty plea which is held in abeyance for a specified amount of time. During that time, the Defendant must complete a domestic violence evaluation and treatment. The treatment is rarely shorter than 36 weeks. During this time the individual is on probation and must report to the probation department, might be required to participate in monitored sobriety, substance abuse treatment, parenting classes, etc. If at the end of the time period, the individual has done what they were supposed to do and not done anything they weren’t supposed to do, then they are permitted to withdraw their plea of guilty and the charge is dismissed.