If you're talking about a component DVD recorder, most have a built in HDD. That way, just like a DVR, you can record the content to the DVD Burner and then burn to disc. I just sold my Sony about two months ago... had a 160 gb HDD.
Oh... and yes, you can record content from a HDTV as long as it's displaying Standard Def content. They won't record HD content. However, if you have your component DVD recorder conected to your cable box via component cables, the standard def image you'll end up recording will actually be relatively decent.
Are you using a cable box? Or are you just using your TV's built in tuner? If you're using your TV's Built in tuner, make sure your TV isn't stretching the Standard Def content to fit your screen. Otherwise, you may end up recording a less than quality image.