Donna,
Yeah that's pretty common. First up when viewing direct from camera to TV that's an 'uncompressed' signal meaning 'you see what is there'. The better your TV, the better your video looks. Once you go to MPEG-2 for DVD you've gone from an uncompressed video to compressed. That meaning in order to fit your video onto a 4.7GB DVD, your NLE software had to discard some of the information contained in the original video.
So in order to make the final output look 'better' on DVD, you'll have to raise your compression levels before you render out to MPEG-2. Now, by raising the compression level you'll be adding back in more video info. Depending on the final length of the video adding back in more info may drastically increase the size of the video file and it may not fit on your DVD. Check with your software manual and look up outputting to MPEG-2 and there should be information on how to raise or lower your compression levels.