Wutai Mountain by train from Pingyao

I understand that the town where the temples are located is actually named Taihuai, and that the commonly named "Wutaishan" train station is actually in the town of Shahe, around 50 kilometers away.

What I am concerned about, particularly with using the train tables on this website, it whether the "Wutaishan" listed on this website's train information is the correct station. According to Google Maps there are several places scattered across China bearing the name WT.

Has anyone taken the train to Mt. Wutai from Pingyao, or Taiyuan, or Datong? Or, for that matter, from Beijing? Was it simple and clear to indicate your destination?

We will also be leaving from Mt Wutai on a train for Beijing... any information you could give me about that trip would also be useful.

Thank you in advance for your help.