True HD is 16x9, with no bars on top or bottom or sides. If you are watching HBO HD, and the picture doesn't fill the screen on the sides, that means that the show you are watching isn't true HD, even though it is playing on an HD channel. When there is bars on top and bottom, that means that the picture has been stretched out (upconverted, or simply converted to fit a widescreen TV), think of it this way, if you took your old TV and grabbed the sides and stretched your TV so that it was now a 16x9, it would have lost height and gained width, the same thing happens to a picture! (remember those screens before a movie would start? Telling you that the film had be fixed so that it would fit on your screen, so in a way I am talking about aspect ratio, just taking the aspect ratio of a 4x3 TV (1.33:1) and making it fill a aspect ratio of a 16x9 TV (1.78:1))
Now aspect ratio is different, 1.78:1 is what an 16x9 TV is, most new movies are made at around 2.33:1, which is why when you watch a DVD that is that aspect ratio you have bars at top and bottom, because the film is wider than the TV, and your DVD/TV have to compress the width and height and hence the bars at the top and bottom.
Take a look at TNT-HD when they play something that isn't true HD, perhaps a TV show or something, if you notice they fill the screen on their HD channel, but, the people have distorted bodies, faces, etc., that is because TNT just stretches the film so that it will fill the 16x9, the same way that you stretch the screen when you watch a SD channel on your wide screen, HDNET Movies when they play a movie with bars on it on top and bottom, that means that they didn't stretch it up/down/side to side, they stretched it side to side only which causes a loss on the height but it doesn't cause distortions (or at least not as much). Old TV shows and movies were not made for HD which is widescreen, someone had to take them and digitize them to make them wider than they were. Which is up converting, I never said that old TV shows aren't good, I was making an argument against the idea that everything is "True" HD, without up conversion! Check out HDTVoice.com, and read some of their FAQs, and some of their post, it discusses how to tell if what you are watching is true HD. It should fill your screen completely, if it doesn't, it isn't actually true HD. Which when you look at Discovery HD, their picture isn't distorted nor does it have bars on it. That is because at least most of the time they record everything with HD cameras and etc...
Now of course they used to have 4x3 HDTV's, and when something was true HD on one of those TV's it would have bars on top and bottom, because just like on DVDs, the width and height had to be compressed, to fit the width of the TV, and because of this there was bars on top and bottom.