(2-part post):
Every 'active' channel (i.e. a channel which is being watched or recorded) needs its own separate tuner. For example, those people who've still got an 'old-fashioned' video cassette recorder with an analogue TV, have two analogue tuners. (One inside the VCR and one inside the TV). So it's possible for them to watch one channel while viewing another.
DVD recorders vary. Some don't have their own tuner. (They take their signal from the TV's tuner, so they can only record the same channels as is being watched).
Some have their own analogue tuner. If so, they can record one of the 5 analogue channels while the TV can be used to watch a different channel. (This channel might be either analogue or digital depending upon the type of TV or TV/Freeview box combination).
Other DVDRs have a digital (Freeview) tuner. If so, the DVDR can record a Freeview channel while a different channel is watched on TV. (Once again this might be either analogue or digital, depending upon the TV, or TV/Freeview box combination, in use).
Even if you've not got a DVDR with an integral TV tuner, you'll still be able to watch one channel, while recording another, if you've got a Freeview box (which has its own digital tuner).