Does TV resolution 720p also mean 1080i?

You are correct.

Most HDTV's will accept 480, 720, 1080 signals. Each different resolution will be up or down converted to fit the "Native Resolution" of that television.

The rule of thumb is most people cannot tell the difference in image between a native 1080 or 720 display if the screen size is below about 40 inches.

"HD Ready" (I am guessing at your next question.)

HD Ready has nothing to do with 720 or 1080 or "Full HD".

Some televisions are marked as "HD Ready". This means you cannot use an antenna directly attached to the television.

Back when they were deciding on the antenna signals - there was a lawsuit that went on for a year or so that challenged the signals.

If the lawsuit passed and the signals changed - all the existing HDTV's would no longer work with an antenna.

TV Makers were upset because they knew the consumers would blame them if their televisions suddenly stopped accepting over-the-air TV signals.

So they removed the antenna/channel-changing electronics from the televisions and created an external box that would accept antenna signals, let the user change channels and pass the video/audio onto the HDTV. If the antenna signals changed, the users would buy another $200 box instead of buying another $2,000 television.

But this caused confusion so they had to mark these special televisions as "HD Ready". Meaning the television was a HDTV and it was "ready" to work with whatever signals they came up with down the road.

They continued to make "HD Ready" after the lawsuit failed because many people use cable/sat box's and never hook up an antenna.

No, if your tv don't produce 1080p you is not going to be equipped to look at a blue ray in 1080p, equal as game. You are Xbox is set to 1080p however your tv will use the max she is ready to provide which on your case is 720p/1080i.

Most TV's under 37 inches are 720p.. You can still watch 1080i content... At that size, you will see little if any difference.. (But the best it can display is 720p.)

It will be able to handle 1080i but it will display it at 720.