Two passengers on the same train can have paid very different amounts, while two passengers on a regional service almost never have. Railways run two different pricing systems side by side.
Regional fares are set by distance
Local and regional services in most European countries price by distance according to a published table, and the fare is the same whenever it is bought.
Those services are usually operated under a public contract with an obligation to provide a certain level of service regardless of how full the trains are.
Because capacity is not the constraint that pricing is managing, there is no reason to vary the fare, and buying on the day costs no more.
Long-distance services use yield management
High-speed and long-distance trains are commercial operations competing with flights and cars, and they price seats the way airlines price them.
Cheap fares are released in limited quantities well in advance, and as those buckets sell out the price available moves upward toward a flexible fare.
The final price is therefore a function of how many people have already booked that specific departure, not of how far in advance the purchase is made.
Reservation requirements distinguish the two
Where a seat reservation is compulsory, the operator is controlling capacity, and yield-managed pricing almost always follows.
Where boarding is open and no reservation exists, the fare is generally fixed, and a ticket may be valid on any service that day.
This distinction is a more reliable guide to how a route is priced than the type of train, and it is stated at the point of booking.
Passes solve a different problem
Rail passes cover the transport right but frequently not the compulsory reservation, which is charged separately and can be limited in number.
Their value lies in flexibility rather than in the lowest possible fare, since advance point-to-point tickets on a planned itinerary are often cheaper.
For itineraries that change as they go, or that use many short regional hops, the arithmetic can move the other way.
Where the cheap fares actually sit
Release dates vary by operator and are usually a fixed number of months ahead, after which the cheapest bucket is available until it sells.
Early morning and late evening departures hold their cheap fares longest, because demand concentrates in the middle of the day.
Splitting a long journey into separate tickets sometimes produces a lower total, though it removes the operator's obligation to rebook if a connection is missed.