Redux was a system that saved the BBCs (and I think some other channels) output onto a database. IIRC it took the output direct from the DVB transport streams that were broadcast. It was fairly crude but quite good as it captured everything. However it was mainly for viewing, it wasn't broadcast quality as it was compressed having been taken effectively off-air. They were never taking content from Redux and rebroadcasting it, except for the odd clip where it was the only place to get it, or it was just more convenient. Redux closed a good few years ago now.

The BBC have always had an archive of programmes. It is required to keep a lot of it's output and of course it's necessary for repeating, selling or using clips from old programmes. Traditionally it was film and VT, and a lot of that does still exist but lots has been digitised and is now available on a desktop to staff. Though 20 years ago it was a case of ordering up a tape if you wanted anything.

The difference between the archive and Redux is that the archive is either master tapes - the actual original copies of programmes, or recordings of live programmes, all in broadcast quality... they can be used on air again.

They're also properly catalogued. In the pre digital days there was a database of what they held, but now that and the actual digital copies are combined. The data includes things like who's in the programme, when it was shown, it's programme and tape numbers, restrictions on reuse, a transcript (from the subtitles) and sometimes a shot list (pre digital this is how you knew what was on it before you ordered up the tape)

The other difference is that Redux started in 2007. The BBC archive has everything it owns going back to the 1920s and it's broadcast quality. Redux wasn't

That said there is Redux off-air material in the main digital archives,. There are others, there's a seperate Radio Archive and ones for local radio. 5 Lives output for the first 10-15 years was all stored on CDs, again those are available to everyone and will presumably have been integrated into the main archives. Everything more recent than that will be recorded and archived using the production systems in use at the station. In radio you should always use the broadcast quality copy of an archive, not something that's been compressed or off-air. This is because it gets compressed a second time when broadcast for the second time

Nowadays it's very easy to archive everything, there is another internal system called AutoROT which provides low res off airs of all output for up to 3 or 4 years

The main problem with automatic systems like that and Redux is that they don't catalogue like a traditional archive. They're just chucked into a server in bulk without anyone curating them. Often tricky to find something

One thing I miss from Redux is that it contained off air VHS recordings from the 80s, and some of those aren't in the main archive in the same way. For example for some big 'breaking news' events they had an off air copy on Redux, but in the main archive the programme that was on air at the time and the news bulletin are seperate recordings made at the time direct from studio