The live view (LV) from the camera uses a different sensor to the main camera sensor (HQ).  The images taken by the live view sensor have a different depth of field, meaning the focus is different between the shots.  The reason there are LV and HQ images to view is because of this fact, the change between the live image and the HQ images is distracting when working.  This is why there are two sets of images, LV (live view) and HQ (high quality).  The HQ images are resized so you can play them back at 30fps.  

They are actual copies of the high res images taken by the camera.  

Live view uses a smaller sensor which has a greater depth of field by its nature (more is in focus) than the larger camera HQ sensor.

On the interface at the bottom right is an button for the DSLR image lab, where you can take test shots and check exposure and focus.  To make more of your HQ images in focus (increase the depth of field), increase the Aperture setting (so, go from 5.6 to 16).  

EO setting on the Camera tab

"EO" (exposure offset) is only for lenses with manual aperture rings, you will not see any change when using a Canon lens. This feature fixes an issue with Canon DSLRs when using manual aperture lenses - they slightly underexpose the the live view on some models.

Watch tutorials we have on the subject:

Which camera should I use?

scroll down to the bottom of the page and check  out the four tutorials.