If a Judicial Release is filed for someone in Ohio and a court date is given for the person to appear, does that mean it will be granted? She is currently in a prison 2 hours from here (where the court date is set). Will they have to bring her for the court date? Does that mean it will be granted given that they wouldn't transport her all that way to deny it?

What you are asking about is probably what they call Shock Probation or something similar to that.

Yes, they will transport her to the Courtroom from prison in order to attend this hearing. Just because the hearing is scheduled is no guarantee that the release will be granted. Yes, they have transported prisoners "all that way" and had their release denied. Not uncommon.

Is she in "prison" or "jail" there is a large difference.

But yes unless it is a civil issue, normally they always transport.