A self-fulfilling prophecy is a prediction that causes itself to become true due to positive feedback between belief and behavior. Although examples of such prophecies can be found in literature as far back as ancient Greece and ancient India, it is 20th-century sociologist Robert K. Merton who is credited with coining the expression "self-fulfilling prophecy" and formalizing its structure and consequences. In his book Social Theory and Social Structure, Merton says:
"The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behaviour which makes the original false conception come 'true'. This specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning."
In other words, a prophecy declared as truth, when it is actually false, may influence people, either through fear or confusion, so that their reactions fulfill the once-false prophecy.
The Pygmalion Effect, or Rosenthal effect, refers to situations in which students perform better than other students simply because they are expected to do so. The effect is named after George Bernard Shaw's play Pygmalion, in which a professor makes a bet that he can teach a poor flower girl to speak and act like an upper-class lady, and is successful. This effect requires a student to internalize the expectations of their superiors. It is a form of Self-fulfilling Prophecy, and in this respect, students with poor expectations internalize their negative label, and those with positive labels succeed accordingly. Within sociology, the effect is often cited with regards to education and social class.
Reference: Merton, Robert K (1968). Social Theory and Social Structure. New York: Free Press. pp. 477.