1080i and 1080p are too vastly different things. There's no such thing as a 1080i screen (it's just a signal type) - the Hitachi screens sort of possibly being the exception.
Any TV (whether it has a 1920x1080 or 1024x768 or 1366x768 panel) has to process 1080i to fill in the missing lines (interlaced signals only send alternate odd or even lines each scan)
How good a job that processing does creating a full frame picture is far more important than how many pixels the panel happens to have.
So you do have a "1080i screen". It always means, "this TV can accept 1080i"
Whereas when people talk about 1080p screens, they nearly always mean a screen that has 1920x1080 pixels, rather than a screen that will accept a 1080p signal (which by the way your Samsung won't, but the PX70 will)
It can be confusing but that's pretty much all there is to it, until you start to ask whether it will take 1080p/24 or just 1080p/60
I heard the difference between a 720p image and anything 1080 is quite vast.
For movies, that's maybe true. A proper 1080p film frame can be rebuilt from a 1080i signal. For video, it's not. 720p and 1080i contain roughly the same number of pixels.
I really wouldn't get too hung up on the numbers, there's a lot of 1080p screens out there which are like a Corsa with a supercharger. Yes it's got a shedload of horsepower but the brakes and suspension aren't going to keep the thing on the road.