TRUE HD? huh?

Now im new to all this HD talk. But ive been playing with my 32 LCD for the last months or so (it was a budget but still expensive brand LCD),said it was HD which support up to 1080p etc (Even though i know Warhawk dont support 1080p)

We just recently got a Sony 40inch, and its like waaaay clearer then my 32"? I can see the stones on the ground n everything
Its so clear that my guy looks 3D and it actually affects the way i play warhawk now? Even feels like the player lags a bit.. Hard to explain lol... Why is it clearer if my 32LCD supports up to 1080p to? Is there different types of HD?

Who here plays with a clear mother bleepIn LCD like this? Is it harder to play with?

Ive converted back to my 32" for gaming
40" for the lounge

Look at the controls on the TV. They probably have some digital signal noise reducer or some other processing effect that is causing lag. My TV has DNR and something else that makes my picture lag slightly.