What is the difference between deep-frozen and frozen food?

Deep-frozen and frozen food is not the same thing.

The distinction is defined in an Italian law on deep freezing (D.L. no.110 of 27th January 1992), but there are other differences too.

What is deep freezing?
Deep freezing is an industrial process carried out by specialist machines, which lower food temperature very rapidly. This rapidity kills micro-organisms and prevents crystals expanding, so that cell structure stays practically intact and the food is preserved without spoiling. Deep-frozen foods keep flavours and nutritional values intact.  So how should we store and consume deep-frozen foods? They must be stored following instructions on the packet, which give temperatures, ways and duration of storage.
What is freezing?
Compared with deep freezing, freezing takes place more slowly and at higher temperatures.
You can freeze food at home in your freezer, where temperatures range from -6° to -30°C. 
The star rating on your fridge gives you the temperature: 1 star = -6°; 2 = -12°; 3 = -20°; 4 = -30°.  So more stars means you can keep food for longer.