I am planing to travel from Geneva, Switzerland to Lyon, France by train. Can I buy tickets at the station, or do I have to book them in advance? If I can buy them at the station, what are the benefits of booking tickets in advance?
I've done a quick bit of research, and am confident enough now to supply an answer. Any locals who find any errors, please do point them out!
If your travel times involve you travelling only on TER (regional) trains (which make up the majority of trains on this route), your ticket is not tied to a specific train (only to a specific date), and for a "TARIF NORMAL" ticket, you can buy a ticket for the same price at the station on the day.
Right now, there also seem to be special offer 40% off fares available at certain times of day (10am-3pm) for TER trains called "BILLET TER HAPPY HOURS -40 %". I don't know if these are available at the station or not, I'm afraid; my French isn't good enough to do this search. I can find that similar offers in the past were only available online or through the app, but I can find nothing about the current one. If your train would be eligible for such an offer, it therefore might be worth buying in advance.
However, since these tickets do not tie you to a specific train, it would always be possible to buy TER tickets on the day, no matter how many people are intending to travel on the same train!
TGV (high speed)
If you intend to travel on one of the few TGV trains per day, these tickets come with a mandatory seat reservation, and you must travel on the train for which your reservation is issued. I can find fares marked (on the English version of the SNCF website) as "Flexible" (formerly called "Pro") and "Exchangeable conditions apply" (formerly called "Loisir") ("Non exchangeable" (formerly "Prem's") tickets are also available for some TGV routes, but I couldn't find any for the Geneva to Lyon route on a few dates I tried, so it's possible these aren't available at all for this route). As far as I can find online, only the "Fleixble" ("Pro") tickets are available to buy on the day at the station. So if you're intending on using one of these few TGV trains per day, it's cheaper to buy in advance.
It's also worth noting that due to everyone getting seat reservations, the TGV trains could theoretically sell out, in which case you wouldn't be able to buy tickets on the day. But whether or not this happens in practice on this route, I don't know.