What is the Difference Between a Rebbe and a Rabbi?

The words rabbi and rebbe come from the same root Hebrew word, rav, meaning teacher or spiritual guide.  Both terms can refer to a teacher of Torah, a personal mentor or teacher, or a spiritual leader. Rabbi is the commonly used word to describe a teacher or mentor in most modern Jewish movements. Rebbe is a Yiddish-German word that connotes a spiritual leader and master of theology in the Hasidic movement. Hasidic Jews refer to the leaders of different Hasidic dynasties as rebbes. A rebbe is required to be a tzaddik, or righteous man, in the eyes of God. Rebbes are also sometimes associated with the Baal Shem Tov who Tzvi Freeman noted was a teacher who not only touched your mind and heart.

Sources: Wikipedia; 
Rav, Rebbe, Rabbi, The Forward, (September 19, 2003);
Rabbi Louis Jacobs.  The Tzaddik, or Rebbe, MyJewishLearning.com;
Tzvi Freeman, What Is a Rebbe? Chabad.org.