to clarify about discounts for seniors - the only way to achieve those discounts of 34% is to purchase a Railcard. There is no such thing as a "senior fare ticket".
Railcards - https://www.railcard.co.uk/ - can also help you decide which if any you want
These cards cost £35 each.
The Senior Railcard is personal to an over 60 individual, does not require a photo, and is valid on most trains of most operators. For the two of you, you will both need to qualify and buy both. Because they are individually personal you can take independent trips and still get a discount. Valid all day every day EXCEPT in London and the Southeast M-F when not until after 9:30.
https://www.senior-railcard.co.uk/
The Two Together Railcard is for any two people of any age who travel together at all times that they use the Railcard. They don't need to be related. A photo of each is required and is applied to the Railcard upon purchase. It gives the same benefits as the Senior Railcard but the 9:30 am restriction is everywhere and for everybody Monday through Friday, not just London and the Southeast. No time restriction on weekends or Bank Holidays. You cannot split up and one keeps the Railcard. You must travel together for the benefit - but you only need one which covers both of you so you break even £100 sooner.
https://www.twotogether-railcard.co.uk/
Cards are valid for exactly one year from date of purchase, unless you buy the 3 year version, and you don't need to have them when you buy tickets - just when you use the tickets. You show both the tickets and the Railcards at the barrier and when checked on the train.
A read of the website will be helpful.
Remember that because each Railcard cost £35 you need £100 of savings to break even, £200 if you get 2 Senior Railcards.
Even without a Railcard you can get lower priced Advance tickets which can be quite cheap. They must, as the name implies, be bought some time in advance, often the cheapest at 12 weeks, but some even as late as the day before (but check) and are for a specific train at a specific time, non-refundable and virtually non-amendable. Measure twice and cut once. Yes, if you have a Railcard you get the discount on these Advance tickets too.