Yes, it is cheaper on their website but only if you choose your train in advance and buy one of the Sparpreis tickets for it. Here is how it breaks down:
* While supplies last (and no later than three days before travel), you can buy Sparpreis-Tickets online. You have to pick specific trains and are bound by these. The price should be from €19 oneway or even less per person if there are two of you going.
* If there is no Sparpreis available and you are traveling within less than a week, you can buy last minute tickets at
http://bahn.ltur.com/ from €24 oneway. The number of tickets is very limited and you have to pick specifc trains again.
If you do not avail of any of the above, you have to pay full price. There are different options:
* Buy a regular ticket online. No surcharge.
* Buy a regular ticket at a machine at the station. No surcharge.
* Buy a regular ticket at the window. Surcharge for bothering a human when a machine would have done (notice this is the opposite of Ireland where you pay a surcharge for the privilege of dealing with a machine).
* Buy a regular ticket on board. Surchage for onboard sale. This is the dearest option with a total surchage of €5 or so.