I hope this explanation isn't too pedantic.
You will be getting 480 (vertical) lines, interlaced, with the NTSC aka analog video. This is where 480i comes from.
I believe the composite inputs/outputs are limited to around 330 (horizontal) lines of resolution, and since the chroma (color) and luma (black and white or brightness) are combined into one signal, your dvd recorder must then separate them with some signal processing, further degrading the quality.
So, your tuner is taking a mpeg-2 stream from the ATSC signal, and converting to a composite analog signal, then your dvd recorder comb filters to get the luma and chroma separated, then I'm guessing these signals are further processed to get the component values, usually made up of three signals.
This is then compressed into a new mpeg-2 stream to be recorded on the disc. As you can see, the original tv signal has gone through a lot to be recorded onto a dvd-r, its not surprising that the picture looks a bit soft after all that.
The recorded picture might improve if you used a converter box that has an S-video output, and connecting that to the S-video input on the dvd recorder. I believe S-video connections can support around 440 (horizontal) lines of resolution. Plus, with S-video, the luma and chroma are carried over separate wires, so there will be less processing needed in the dvd recorder, giving better quality than composite video.
With your composite lines, you are getting 330 (h) X 480 (v) lines of resolution, and S-video getting 440 (h) X 480 (v) lines.