WHAT IS THE DIFFERENCE BETWEEN BEGIN AND START?

They are  synonyms and mean the same thing.

Synonyms: begin, commence, start, initiate, inaugurate

These verbs denote coming into being or taking the first step, as in a procedure.
 Begin, commence, and start are equivalent in meaning, though commence is more formal, and start often stresses the point where inaction turns to action:
The play begins at eight o'clock. The festivities commenced with the national anthem. We will stay on the platform until the train starts.
Initiate applies to causing the first steps in a process: I initiated a lawsuit against the driver who hit my car.
Inaugurate often connotes a formal beginning: “The exhibition inaugurated a new era of cultural relations”