There's a few things going on here.
The two HDTV resolutions are 1280x720 and 1920x1080.
First, manufacturers use the term "720p display" in their marketing literature loosely and incorrectly. These days, they tend to use it for anything that isn't a "1080p display". So let's put that one to rest first.
The native resolution of a 1366x768 panel is not 720p. If anything, it is 768p, since all input is scaled to the 768 lines. But, of course, 768p is not a resolution that is used in the source material. Only 720p and 1080i/p are used. We should count 480i/p also, for SD material and DVDs.
In the case of plasma, it is fiendishly difficult to make plasma panels with small pixels. This is why 1080p plasmas are so long in coming and why 42 inch plasma panels are 1024x768.
How can 1024x768 be HD, you ask. Many dozens of people have asked that over and over here in the forum. The answer is, the Consumer Electronics Association has decided that any display with at least 720 lines can be called an HDTV and have the logo. There is some basis in fact for this because the human eye is more sensitive to vertical resolution than to horizontal resolution. This has been taken advantage of for years in NTSC because the horizontal resolution of NTSC is really poor. It is also taken advantage of in so-called HD-lite where the video is resampled to 1440x1080 on things like satellite, or maybe even shot with a 1440x1080 camera instead of the 1920x1080 camera you thought the network was using, and you probably didn't even notice.
We have had intense wars about whether that CEA definition is legitimate. Believe what you will, and if you don't think 1024x768 is HD, buy something else. Vote with your wallet. Simple as that.
In the case of LCD, it is difficult to make large pixels. This is one reason why 1366x768 has been used. Also, please do not forget that a lot of HD is in 1080i, so 1920x1080 has to be downscaled to 1366x768. Conversely, 1280x720 has to be upscaled to 1366x768.
To those who say, but wouldn't it be a good idea if the panel were 1280x720 so at least one of the resolutions wouldn't have to be scaled, I say nope! For one thing, you'd be downscaling 1920x1080 all the way down to 1280x720, so you'd lose a lot of resolution on the very format that is supposed to be giving you lots of detail, which is also what most channels broadcast in. For another thing, the extra resolution is really helpful on things like diagonal lines, where you can smooth out the line. If you were in 1280x720 on a 32 or 37 inch display, you'd probably be complaining that the display looks all blocky and pixelated because the pixels are just too big and the diagonal lines have too much stairstepping.
Turns out you can get 1280x720, but you have to go all the way down to 22 and 23 inches, where it works nicely.
Oh, and one other thing that comes up over and over again. The resolution of 1080i is not "540p", it is 1920x1080, dang it. If you were to shoot a still life, you would have 1920x1080 worth of pixels. It's simply that you have to wait 1/30 second rather than 1/60 second to get all the pixels. If it's a live shot. If it's film, it was shot at a mere 24 frames per second, so (inverse telecine, 3:2 pulldown, which is actually reverse 3:2 pulldown) done correctly gives you back your movie.
