HDTVs, unlike monitors, also have "Picture Mode" options (ie. Standard, Theater, Sports, PC, etc.) which also affects the display size on the screen. You may think it's the PC mode that you should use but that one is only if you are using VGA cable and not HDMI cable.
On my Win 8 HTPC which is connected to my 47" living room HDTV via HDMI cable, I have to set the picture mode to "Game Mode" to be able to fit the resolution perfectly in the TV screen. You may want to explore that feature on your HDTV.
The other possibility that I see is maybe that your GPU is not capable of outputting "interlaced" video (1080i) which is basically like half the "progressive" video resolution (1080p). So, you should actually be looking at the lettres "i"...