I've no idea where Eddie is getting his information from but it seems to be extremely unreliable!
A Senior Railcard costs £30 per year (either online or from a rail station) or £70 for three years (online only). However some local authorities offer it at a discounted price when purchased from their offices. (I assume that's where Eddie's figure of £20 comes from).
The qualifying age for a Senior Railcard is 60 and, since it's offered by the Association of Train Operating Companies (rather than by any governmental body), that age is unlikely to change. It gets the holder 34% off almost all National Rail fares (including those that involve travel on London Underground services although it can't be used just for single Underground journeys).
A National Bus Pass gets the holder free travel after 0930 (or any time at weekends) in his home nation only (i.e. England, Scotland, Wales or Northern Ireland). Some local authorities also permit free travel within the holder's local council area before 0930 but the number of councils offering that concession is now far lower than it used to be, owing to cutbacks.
Further, some local authorities also have separate arrangements with local train operators, giving the holder either free or reduced rate travel on LOCAL trains only (NOT nationally) but, again, there are now far fewer local authorities with such arrangements than there used to be.
The qualifying age for a National Bus Pass in Scotland, Wales and Northern Ireland is fixed at 60 but in England it's rising in line with the State Pension Age for women (so I won't get my bus pass until I'm 63-and-a-bit and others will have to wait until they're 65, 66, 67 or 68, dependant upon when they were born).
For those of us who're currently old enough to qualify for a Senior Railcard but not for a National Bus Pass, it's worth noting that 'Plus Bus' tickets (which give unlimited travel within a specified area when you've arrived there by train) attract the same 34% discount as rail travel does. For example, if I travel to Cambridge by train I can buy a Dayrider ticket on a bus there for £4.10 but it's cheaper to get a Plus Bass ticket from the conductor on the train. It would normally cost £3.30 but my Senior Railcard takes that down to just £2.20.