Ive never seen "HD Ready" refer to 720. As I remember it, HD Ready meant that the TV was HD (720 or 1080), but it didnt include an ATSC or QAM tuner. It was more like a monitor than a true TV.
The distinction I've seen with 1080p is calling it True or Full HD.
Actually, it referred to 768, as that was the number of lines that the cheap panels had. Which meant that even to display 720p content you had to scale it.
The distinction I've seen with 1080p is calling it True or Full HD.