If you buy an advance ticket, it's for a particular train and particular connections. If you get on the wrong train, you'll have to pay the full fare which can be significantly higher (My best deal is Montrose to Durham next May for £6.45. the full fare is over £100, so it's best not to miss that train.)
You can save large amounts of money with advance tickets and get very cheap upgrades to first class, but if you miss the train and it's not the rail system's fault, then you're financially stuffed.
The ticketing system is very complicated and often quite illogical - when I was searching for Montrose-Durham trains, at one point the fare to King's Cross from Montrose was just £11, whereas the much shorter trip to Durham on the same train was over £80 and I wasn't allowed to get a ticket to King's Cross and get off at Durham (!) . A few days later, East Coast trains started selling very cheap tickets.
It's madness. Good luck with it!