What Switzerland has is a nationwide mass transit system. It is used by lots of people on a daily basis to go to work, go shopping, go to school etc... Having to buy tickets in advance, having tickets tied to particular trains etc... does not fit with that kind of usage.
So when comparing with the US think of commuter rail not Amtrak. Getting from ZRH to Luzern is as trivial (if not even easier) as going from JFK to Manhattan...
When you buy a ticket on line you usually start with looking up a schedule, and then picking a trains from that schedule. This is just so that you can ascertain yourself beforehand that what you want to do is actually possible. That there is a train for the route and the time of your travel. But an normal ticket will then be valid on all trains on the route, and even allows you to interrupt your journey. It is valid for a whole day, till 5AM the next day.