Actually, its slightly different. When using a DVI or HDMI connection, the display (TV) actually tells the video card what resolutions it can accept. For a TV, normally only the HDTV resolutions are allowed, for example:
1280x720 at 50/60 Hz
1920x1080 at 25/30/50/60 Hz
This data is contained in something called the EDID. So the video card will choose one of these valid resolutions to send to the display.
But, as you are probably aware, most video cards are able to "scale" any desktop resolution to fit the actual resolution of the TV or display. This is similar to laptop screens - lets say the laptop screen resolution is 1024x768, but you are playing an old game that supports only 640x480. Does the game display on only a small box in the middle of the laptop screen? In most newer laptops, no. The laptop's video card will most of the time have an option to "scale" other non-native resolutions (not the resolution of the screen) to "fit" the screen - but of course the non-native resolutions will not look as sharp.
Now back to your HTPC. Some video cards (like the ATI cards) will allow you to choose PC resolutions like 1360x768 even though your display is a HDTV connected using HDMI (which only allows HDTV resolutions like 1920x1080). The video card will then resize your desktop to "fit" the 1920x1080 signal being sent to the TV, so it appears full-screen on the TV. So if you check your Windows Display properties it says maybe 1360x768 but if you check on your TV what signal it is receiving it might say 1080p (1920x1080).