HD DVD is high quality?

Hi people,
When I choose DVD HD in compressor to burn in DVDSP, does that mean that I need a special HD DVD disc or that I'm going to put an HD file into a standard DVD disc?
And the consecuent question is, HD in a standard DVD disc is not anymore HD? Or depends of where I'm playing it?

All that is a bit confusing for me.Thanks a lot for your always valuable help!