What is the difference between an adjudication and a competition?
There is a big difference. Adjudication is usually done through the public schools. In New York State, NYSSMA (the New York State Schools of Music Association) publishes an enormous handbook that provides pieces for each grade, for each instrument, etc. Adjudication is mainly about achieving a level, similar to passing from one year to the next year at school. The Competition is a contest to acknowledge and to reward the best musicians and performers available, and seeks and rewards only the highest level of achievement.