A trial confirmation is a sort of conference which is held to see if the parties can reach an agreement or resolution of the case. If they cannot, either one or both can confirm to the court that they will be going to trial. The judge then tells the Jury Commissioner who makes sure that there will be a jury pool available on the date set for trial. This kind of pre-trial conference is required by the California Rules of Court.
The only thing I can imagine for a "re-trial conference" is that the case went up on appeal or a writ and was sent back to Superior Court for a new trial. That would be called a "retrial."
In Sacramento, the trial confirmation is known as the trial readiness conference or trial settlement conference. If a trial date is just being confirmed, the in custody defendant does not make an appearance in court because his or her presence is not required. If the trial is going to be continued, then the in custody defendant has to be present to agree to the continuance or what we call "entering a time waiver". Don't know how they handle things in Clovis though.
Could there be a retrial as a result of a hang (jury couldn't reach a unanimous verdict). If that's the case, there's often an opportunity in between the first trial and second trial for the prosecution and defense to settle or go to trial again. The prosecution's offer will likely be better after a hang.