ALL MARKETING TERMS. They don't REALLY mean anything technical.
You really want to look at the display resolution, of both a TV or monitor. Technically speaking they are both JUST displays. A TV has a tuner though.
The native resolution of 720P is 1280x720
The native resolution of 1080i/P is 1920x1080
However TV's come in different resolutions just like Computer monitors do. Even though they are 1080 TV's does not neccesarly mean they are 1920x1080 resolution. However, if it says FULL HD 1080 it probably means it is a 1920x1080 resolution display. HD ready would just mean it accepts an HD signal. You will have to look at the specs to see what resolution it is and if it can display 720p/1080i/or 1080P images.
The difference between the i and p are as follows:
i= interlaced picture. This means every other odd row of pixels is displayed every 1/60th of a second, and then switched to the even row. Back and forth.
P=progressive scan. This means that the entire image is refreshed each cycle. Whether it be a 60Hz, 120Hz, etc TV
A computer monitor is always progressive scan, as they are usually 60Hz refresh rate, at least. So a 1920x1080 res monitor can display 1080P content. They may also advertize a 1920x1200 display as full HD, because it exceeds the resolution of the 1080P specification.
in the end, it is ALL just marketing. What sounds better a movie in HIGH DEFINITION, or a movie at 1920x1080 at 60Hz progessive scan?
To answer this, the display IS 1920x1080 60Hz which means it CAN display 1080P content. However, you have to have 1080P content to display. This means you would need to have a Blue Ray player or a digital copy in 1080P format. As far as non movie related items like games. Whatever you set the resolution at, that is what it will display at.