First of all, after lurking for a couple of years, this is my first post. I truly thought I understood the difference between 1080i or 1080p as well as 720p, but now I'm confused. If I understand what is being stated correctly, there is actually no such thing as a 1080i monitor, but only 1080i source material??? Does this mean that you can either have a 720p monitor or a 1080p monitor?
Not quite. An HDTV is a 'fixed pixel' device which means it has a fixed number of pixels - known as its native resolution. That resolution might be an exact High Def resolution like 1280 x 720 (720p), 1920 x 1080 (1080p) or another odd, but common, resolution like 1366 x 768 (which would be 768p - because all HDTVs are progressive scan).
Regardless of the resolution of the incoming signal, the TV will scale it to its native resolution and also deinterlace (convert to progressive) if necessary.
So, yes there is no such thing as a 1080i TV. For one thing, all HDTVs are progressive scan. When people say they have a '1080i TV' what they are really saying is that the highest resolution it can
accept as input is 1080i. The resolution of the TV itself cannot be 1080i because they are all progressive scan.
If the TV resolution is 1080p but can only accept 1080i as input (like the Toshiba HL167 models), the TV will deinterlace the 1080i to 1080p and display it. Likewise, if the TV resolution is 1366 x 768 and it accepts 1080i as input, it will deinterlace the 1080i and then decimate (reduce) the resolution to 1366 x 768.
Incidentally this is why upscaling DVD players and receivers are all the rage. The idea is that the receiver/dvd player can do the scaling to match the TV native resolution so the TV doesn't have to touch it. IFF the receiver/player does a better job of it than the TV, it will be a benefit.