The single fares are not discounted if you use your railcard. All that changes is the daily price cap.
For example, the price cap without a railcard is something like £8. Which means if you do single journeys all day, you won't be charged more than £8.
But if you add your railcard, the cap is lowered, to something like £5, so you will not be charged any more than £5.
+will1337 As I understand it, the price of a Day Travelcard is what they will cap you at, but only for the zones travelled through. So if you only went through zones 1 2 and 3 on your journeys for that day, you will only be charged the price of a zone 1-3 Travelcard instead of a 1-6 one.
Sorry if anything I have said sounds incorrect, but the TFL website is very confusing, especially as some pages still say you can only use it on some national rail services!