To get the clearity of HD, you need to avoid converting anything to anything else. So, the ideal is to take a 1920x1080 picture and display it on a 1920x1080 display.
If the set has 1920x1080 pixels then you'll get full HD. Otherwise, the set downscales the picture to fit the available pixels. This can cause distortions. It's not HD.
Can't agree with that Technologist. I have a HD Ready set, incorporating 1366 x 768 lines of resolution. Yes when I watch HD DVD or Blu Ray films on it, it downgrades the 1080p signal to fit the resolution, but this does not mean it's not HD. It is still HD. The evidence is there to see clearly while watching. Amazing detail and colour. Way better than SD.