This summary is not the rule. The rule text controls.
Each local court decides how trials get scheduled. There are two ways this can happen. The court can set a trial date on its own, but it has to notify everyone involved. Or one of the parties in the case can ask for a trial date, and then that party has to let the other side know about the request.
If a state law says certain kinds of cases should go to trial faster than others, those cases get to jump ahead in line. For example, some cases involving urgent matters or specific legal deadlines may have priority over regular civil cases.
What this means for you is that you don't always have to be the one pushing to get a trial date. The court itself might schedule your case and simply notify you. But if you want to move things along faster, you or your attorney can file a request asking for a trial date, and the other side must be told about it. Either way, you should receive notice before a trial date is set, so you have time to prepare.