What is the exact difference between breeze and wind?

There isn't a difference, a breeze is a wind. Wind is a collective term, breeze is discriptive.

breeze

—n., v., breezed, breez•ing.
—n.
1. a wind or current of air, esp. a light or moderate one.
2. a wind of 4–31 mph (2–14 m/sec).

wind

—n.wind, Literary wînd;
—v.wind), [key]
—n.
1. air in natural motion, as that moving horizontally at any velocity along the earth's surface: A gentle wind blew through the valley. High winds were forecast.

There is a HUGE difference if you are in the same room with someone who is "breaking wind."