The fare from Ceske Budejovice to Ceske Krumlov is just CZK40.00 (£1.42) for a single. Not sure what that fare is you are looking at as it costs nowhere near that much. No need to use apps. You can just buy the ticket onboard the train. Those trains have a ticket machine onboard.
I can't even replicate a price that high on the Můj Vlak app - it's 78kč on there (£2.76).
The disparity however between that and the fare you're quoting will be down to the fact that the 78kč one is the 'OneTicket' tariff while the cheaper one will be specific to the operator or regional transport authority. So, that 78kč will get you on a GWTR service or the daily IC service.
Sometimes Můj Vlak will sell at both tariffs (though it'll automatically suggest the cheapest) and other times it just has the OneTicket one. It can even cope with the different validation behaviours (eg. Ustecko Kraje tariff tickets won't become visible until departure time and function like mTickets).
OneTicket is however a useful option to have as it came about as a result of the network being carved up when the regions started awarding contracts to private operators. It isn't always the cheapest option but means that a through fare is always available no matter how many operators are involved, and that you'll be able to use any operator along that line of route, including in the form of a Day/Week pass for the entire country.