I'm going to stop apologising for giving egg sucking lessons as you give the impression that you might find them useful  ;D
DVD-R discs can be written to once.  You cannot re-record over stuff you've already recorded.  This is fine for stuff you want to keep permanently (like The X-tra Factor that you may want to watch over and over and into your doteage)  :o
DVD-RW discs allow you to re-write over the top of stuff you've already recorded like East Enders if you're gonna be out when it's on but once you've watched it when you get home, you won't want to keep it (?) so you can record over it with new stuff.  In this sense it's more like a hard disc and that's why I brought it up.  It may be that you don't need to buy a hard disc recorder.  Just use DVD-RW discs and then decide if you want to keep what you've recorded or not.
The 2x, 4x, 8x etc. refers to the speed of recording and needn't be an issue.  It would help if you could say what make and model of DVD recorder you've bought then we can find out what it's capable of.
(I'd get her a small box of chocs as well just in case)  :-*