I've read it all and I didn't understood if it is claiming that people can in fact differentiate between 720p and 1080p or not.

I can EASILY see the difference between 720p and 1080p at 37 inch screens and above. EASILY. My friend has a 37 inch 720p screen and I have a 37 inch 1080p screen and the XMB looks like utter crap on his screen after getting used to it on mine.

People that think there isn't a difference obviously haven't had the chance to compare them properly.

720p is just half HD.
But people calling it HD anyways to help sales TV and players.

then what do you consider 480p? beginners HD? lol

I really hate the whole HD terminology anyways. Its utter crap. The TV resolutions are false resolutions to accomidate for piss poor space managment and wasted pixels on TVs versus computer monitors. The sad part is due to the "HD" crapulution computer monitors have been sent on a downward spiral to the same fate TVs have. I really dont understand why the 16:9 resolution even came to be popular. It cuts down verticle space that any film camera can take advantage of but is cut down to fit in the 1920 x 1080 space.  The true screen resolutions should be in the 5:3 or 4:3 space which would allow the verticle cut-of to never happen. Trustfully I'm even confused on why TVs are using the 17:9 resolution at least since IMAX uses it. Using 17:9 would mean that the resolution would be 2048 x 1080 or 2K which is exactly half if IMAX's smaller 4K theaters or within scaling of their 4K+ theaters allowing for better scaling of scenes when downscaling footage to lower resolutions. 

HD = High Definition

By that very term it has always been HD, perhaps the real problem is they should have clarified 1080p as a different spec.  I don't think it is so much a probelm though as all the dodgy wranglings where you have 1080p TV's that can accept a signal of 1080p but only display in 720p (panels aren't 1920x1080 resolution).  Same with TV's that display at 120HZ and above yet cannot accept input signals above 60Hz.  It's about time they all got together and produced a proper true set of specifications that are in the consumers best interest.

This , but i like to add i didn't compare anything but from playing Uncharted 2 and KZ2 i saw the difference easily.

I've a 42" 1080p HDTV in my bedroom and a 37" 720P HDTV in my sitting room and games definitly look better on the 1080p TV. Not by much but you can definitly notice it. Also I sit about 6 feet from both TVs when I'm playing and I could see which lines were jagged and which crosses were dotted from the same distances I play from

U can see difference between 720p and 1080p HD movies.
Most games are 720p so u wont see difference on 1080p TV.

720p is easily distinguishable...if you put a 720p picture and a 1080p picture side by side...

My point being, it's easy to misidentify them if you don't have another reference.

They are that much alike, there isn't much of a difference.

420p is SD
1080p is (Full) HD
720 is just filler since jumping directly to 1080p is rather costly.