Buses, arg!

I should think the website one is the more up-to-date.

Timetables don't really matter much during the day, when the main routes (e.g.25) are very high frequency. Traffic problems often cause curtailments. This is done to ensure that buses are running where needed and that drivers don't exceed their driving time.

Timetables seem to be an excellent source of lavatory paper for the senior managers here...

Bus companies have two timetables - one is the public one posted at bus stops, the other is called the 'compliant timetable'.
The compliant timetable forms part of the official contract between the bus operator and TfL, and is the one the bus driver will actually be scheduled and monitored against. You will probably find that the website is based on the compliant timetable, hence the differences.
It's a bit like LUL, with it's working timetables (staff only), and public times which you see at stations.

Right - 'Countdown' works something like this:

On the radio display on board the bus (as a passenger you may be able to see it) there will be three sets of numbers* - Countdown uses this information as the basis for what you see displayed at the bus stop. This information is also used by the buses network control centre when emergency calls are made by the driver.
Because the network control centre may receive an emergency call with no speech (ie driver is getting a beating), they have to know a rough location of the bus - so the radio must have a route number programed. Countdown cannot tell if a bus is in/out of service or short tripping, it just picks up the route number and displays it at the bus stops.

Like the train describers on our platforms, sometimes they can be useful, other times they cause more hassle than necessary. And it's always sods law it's hassle when it's raining!
Of course I never drove buses like that ( ) You've reminded me of little story - I was driving a bus on a tube strike day (bloody underground workers!), was getting near the end of my shift and was thorouhly peed off with people asking questions. I pulled into a stop and a man asked where my bus was going. As sarcastically as I could, I told him to read the front - to which he replied "i'd love to, but i'm blind". It taught me a thing or two thats for sure

* = smaller operators on the outskirts of London have a less sophisticated version which just displays the company name, and is therefore not used for Countdown.