The terms HD Ready and Full HD are confusing. What they actually mean is 

HD Ready - refers to any display that is capable of accepting and displaying a high-definition signal at either 720p, 1080i or 1080p using a component video or digital input, and does not have a built-in HD-capable tuner.

Full HD - refers to a display which is capable of 1080p

So a TV can be HD Ready and Full HD