There are a number of different people who serve special roles in the Jewish community.
A rabbi is not a priest, neither in the Jewish sense of the term nor in the Christian sense of the term. In the Christian sense of the term, a priest is a person with special authority to perform certain sacred rituals. A rabbi, on the other hand, has no more authority to perform rituals than any other adult male member of the Jewish community. In the Jewish sense of the term, a priest (kohein) is a descendant of Aaron, charged with performing various rites in the Temple in connection with religious rituals and sacrifices. Although a kohein can be a rabbi, a rabbi is not required to be a kohein.
A rabbi is simply a teacher, a person sufficiently educated in halakhah (Jewish law) and tradition to instruct the community and to answer questions and resolve disputes regarding halakhah. When a person has completed the necessary course of study, he is given a written document known as a semikhah, which confirms his authority to make such decisions.
When I speak generally of things that were said or decided by "the rabbis" or "the sages," I am speaking of matters that have been generally agreed upon by authoritative Jewish scholars over the centuries. When I speak of rabbinical literature, I speak of the writings of the great rabbis on a wide variety of subjects.
Since the destruction of the Temple, the role of the kohanim has diminished, and rabbis have taken over the spiritual leadership of the Jewish community. In this sense, the rabbi has much the same role as a Protestant minister, ministering to the community, leading community religious services and dealing with many of the administrative matters related to the synagogue.
However, it is important to note that the rabbi's status as rabbi does not give him any special authority to conduct religious services. Any Jew sufficiently educated to know what he is doing can lead a religious service, and a service led by such a Jew is every bit as valid as a service led by a rabbi. It is not unusual for a community to be without a rabbi, or for Jewish services to be conducted without a rabbi, or for members of the community to lead all or part of religious services even when a rabbi is available.
A chazzan (cantor, pronounced with that throat-clearing "ch") is the person who leads the congregation in prayer. Any person with good moral character and thorough knowledge of the prayers and melodies can lead the prayer services, and in many synagogues, members of the community lead some or all parts of the prayer service. In smaller congregations, the rabbi often serves as both rabbi and chazzan. However, because music plays such a large role in Jewish religious services, larger congregations usually hire a professional chazzan, a person with both musical skills and training as a religious leader and educator.
Professional chazzans are ordained clergy. One of their most important duties is teaching young people to lead all or part of a Shabbat service and to chant the Torah or Haftarah reading, which is the heart of the bar mitzvah ceremony. But they can also perform many of the pastoral duties once confined to rabbis, such as conducting weddings and funerals, visiting sick congregants, and teaching adult education classes. The rabbi and chazzan work as partners to educate and inspire the congregation.
A gabbai is a lay person who volunteers to perform various duties in connection with Torah readings at religious services. Serving as a gabbai is a great honor, and is bestowed on a person who is thoroughly versed in the Torah and the Torah readings.
A gabbai may do one or more of the following:
The kohanim are the descendants of Aaron, chosen by G-d at the time of the incident with the Golden Calf to perform certain sacred work, particularly in connection with the animal sacrifices and the rituals related to the Temple. After the destruction of the Temple, the role of the kohanim diminished significantly in favor of the rabbis; however, we continue to keep track of kohein lineage. DNA research supports their claims: a study published in Nature in June 1997 shows that self-identified kohanim in three countries have common elements in the Y-chromosome, indicating that they all have a common male ancestor. For more information about this and other recent genetic studies, see The Cohanim/DNA Connection at Aish.com.
Kohanim are given the first aliyah on Shabbat (i.e., the first opportunity to recite a blessing over the Torah reading), which is considered an honor. They also traditionally recite a blessing over the congregation each Shabbat or at certain times of the year.
The term "Kohein" is the source of the common Jewish surname "Cohen," but not all Cohens are koheins and not all koheins are Cohens. "Katz" is also a common surname for a kohein (it is an acronym of "kohein tzaddik," that is, "righteous priest"), but not all Katzes are koheins.
The entire tribe of Levi was set aside to perform certain duties in connection with the Temple. As with the Kohanim, their importance was drastically diminished with the destruction of the Temple, but we continue to keep track of their lineage. Levites are given the second aliyah on Shabbat (i.e., the second opportunity to recite a blessing over the Torah reading), which is considered an honor. The common Jewish surnames "Levin," "Levine" and "Levitt" are derived from the tribal name "Levi," but not all people with these names are Levites and not all Levites have surnames that suggest the tribal affiliation.
Rebbe is the term for the spiritual master and guide of a Chasidic community. The term is sometimes translated as "Grand Rabbi," but literally it simply means "my rabbi." A rebbe is also considered to be a tzaddik (see below). The position is usually hereditary. A rebbe has the final word over every decision in a Chasid's life.
Outside of the Chasidic community, the term "rebbe" is sometimes used simply to refer to ones own personal rabbi or any rabbi that a person has a close relationship with.
The term "rebbe" should not be confused with the term "reb," which is simply a Yiddish title of respect more or less equivalent to "Mister" in English.
The word " tzaddik" literally means "righteous one." The term refers to a completely righteous individual, and generally implies that the person has spiritual or mystical power. A tzaddik is not necessarily a rebbe or a rabbi, but the rebbe of a Chasidic community is considered to be a tzaddik.