Upconverting player is making assumptions about what the pixels would be that are missing between the lines of pixels that do exist. A standard DVD Video player outputs in 480i or 480p resolution and the content might be about 576p (if it is PAL not NTSC). That means that about half of the lines are missing when upconverting from 480p to 720p. As the upconverting player makes its assumptions it might put a gray pixel between a white and black pixel. But what if the pixel is not supposed to be gray but instead white or black? Now you realize that it is not the same. That is the difference between 720p native and 480p upconverted to 720p on a 720p set

Blue Ray DVDs are capable of 1080p resolution. So the content looks much better on a 1080p set. But all of this assumes that the movie in this format originated with at least this much resolution. You would not want an upconverted movie title as your standard for judging this whole medium.

Yes, there is a difference between upconverting and true HD. Visually, it may not be much.
Blu-ray is another form of HD that is a joint project between Sony, Panosonic and Toshiba(I believe). The advantage to Blu-ray is that so much more data could fit on one disc. (25GB for a single layer.) The higher capacity allows more picture detail to be recorded to the disc.