Teletext and BBC Red Button are essentially the same, just with quite a few lick of paints. I think you can still access Red Button to this day?
The BBC's service was branded "Ceefax", ITV and Channel 4 branded theirs "Teletext".
The current 'red button' service is a completely different protocol running on DVB (Digital Video Broadcast, i.e. digital TV). Text packets are added to the MPEG-2 stream.
In France most IPTV operators still use teletext for live subtitling because it eats much less bandwidth than dvbsub
Red Button is the service that replaced teletext/ceefax in 2012. Teletext was an analogue service, Red button was a whole new digital service offering similar information, it’s entirely different infrastructure underneath, it’s not just a “lick of paint”.
Teletext was a _digital_ service provided over an _analogue_ bearer - the modulation of the signal is continuous, not discrete.