This video thing is more complicated than I thought.
Yes it is. h264 can also be encoded at various bitrates for both video and audio. Most video recorders (camcorders, cameras, etc.) record at the highest and uncompressed quality possible. After transferring the video to a computer you can very likely re-encode it at the same quality but smaller file size (and likely easier playback for older devices).
Can I burn a HD video on my computer harddrive to a DVD and play the DVD on my DVD player?
Absolutely right the right software. Mind you that you would be losing quality going from high definition to the standard definition that is DVD. I've found that the most simple way to share videos is to just upload it to my YouTube account and set it as private URL shared only.