Correct, and for those who don't know the difference between a field and a frame, a field is half the resolution of a frame. (1920x540) Each field alternates between odd and even lines of the original 1920x1080 image at DIFFERENT points of time. To make up for the missing data, you have to deinterlace the image back into a progressive image which features a bit of image interpolation, so you can't truly ever get the original image unless the original content is 30fps or lower to begin with. (Because you could technically stuff 30 full frames into 60 fields per second with no loss of the original resolution.)
If you convert a 720p/60 frames per second into a 1080i/60 fields per second image, you're going to lose image information any way you look, even with the best deinterlacer... but the better ones can make better guesses... same goes for 1080p/60 frames per second to 1080i/60 fields per second.
I know it's super technical, and it's better to just Google "What's the difference between interlaced and progressive" or "What is deinterlacing" if you want to learn more. :P
But, yeah, basically on any progressive display, you would prefer 1080p to 1080i, and 720p even to 1080i (at least, when you're not watching a low frame rate movie)
Games, Sports, and any other "video" type that runs at 60fps, you always want to use progressive. Being forced to a special "Game mode" to watch these things without motion artifacts on the Sharp really should be addressed by them as soon as they can.