I already watch TV through a Freeview box, and want to be able to record anything from it. Do the analogue ones just work for the terrestial channels? Would I need a digital one, even though I already have a Freeview box?
You need a freeview one with at least a twin tuner.
If you have an alogue one, you will have to set it to record either AV or EXT and you won't be able to watch a different freeview channel whilst you record.
The only reason your old video recorder could record one channel whilst you watched another was because it had its own tuner - it's exactly the same for digital tv.