Not ON =but WITH. Its a pass that is valid for about any major railway in Europe-west of the Russky borders. Many long-dist trains also need to be reserved at extra cost (or often more trouble). You will never ever see a train labelled EUrail-though there is EuroBahn (IN Germany).

IF this is the only trips you intend to take and assuming you’re senior? then simply buying advacne tickets (easier to get online) may work out cheaper. Visit seat61.com for info howtodo that, varies per country. But then you tie you in into a fixed advance set itinerary