The first place to start is "HD" and "Full HD" - both sound impressive but they don't mean the same thing.
Full HD means the television screen is 1920 pixels wide and 1080 pixels high, often referred to as 1920x1080 or 1080p. This is the resolution of Blu-ray movies. The high definition digital TV and Foxtel channels are mostly in 1080i. The "i" refers to interlaced which means the television rapidly switches between displaying every second line, whereas "p" for progressive means every line in displayed in every frame - offering a smoother picture.
If a television has HD written on it but not Full HD, then it probably has a widescreen resolution of 1280x720 - often referred to as 720p. It's possible that the television can still take a 1080p signal and downscale it to 720p, otherwise you can probably change the output settings on your Blu-ray player or HD set top box.
Some high definition content is broadcast in 720p rather than 1080i, such as Foxtel's US sporting channels like ESPN HD.
Generally speaking the more pixels you can get the better, although it's worth keeping in mind that a good 720p plasma will often look better than a cheap and nasty 1080p LCD.
If a television doesn't have a HD or Full HD sticker on it, then it's probably standard def television with a resolution of 720x576, or 576p - the resolution of DVD and standard-def television. Watch out for some bulk discount stores selling ultra-cheap LCDs which are actually 480p - sometimes called EDTV (Enhanced Definition TV). Stay away from such televisions, as they aren't even sharp enough to do standard-def digital justice.
The government also introduced a new television labelling scheme this year to help shoppers understand what kind of digital tuners a television has.
Watch out for the blue "Digital Capable" sticker, which means the television doesn't actually have digital tuners. Digital Capable means it's an analog television that can display the digital channels if you hook it up to a digital set top box. It probably can't display the high-def channels in 720p or 1080i, but if your set top box has high-def tuners it should be able to downscale these channels to 576i or 576p to display on the television. Not that it matters much - as the high-def channels tend to be 24 hour simulcasts of the standard-def channels these days.
The yellow "Digital Ready - Standard Definition" sticker means the television only has standard-def digital tuners. This means you won't be able to watch the five high-def channels, which is obviously disappointing if your television has a resolution of 720p or 1080p.
The purple "Digital Ready - High Definition" sticker means you can get all the standard and high-def digital channels.