Answer:
   
   The term "Traditional" has often been used as a synonym for Orthodox
   (especially when using the dichotomy Traditional/Liberal). However in
   recent years this useage has become less common: A faction broke off
   from the Conservative movement, and took the name "The Union for
   Traditional Judaism" (UTJ); its members are known as Traditional Jews.
   UTJ is a trans-denominational organization, working with the broad
   spectrum of Jews, and is not part of Modern Orthodoxy or any other
   denomination. Their "hashkafa" is in line with what many people might
   think of as Modern Orthodox, although in some ways it may be the left
   of standard Modern Orthodoxy and in other ways it may be to the right
   of Modern Orthodoxy. They shun denominational lables in order to get
   beyond the politics of religion, so that they can work with all Jews
   in supporting the practice of halachic Judaism.
   
   Note also that the Conservative movement in Israel and Europe is
   called Masorti (Traditional) Judaism. As such, fewer people use the
   term "traditional" without additional qualification, so as to avoid
   confusion. In the FAQ, the term "traditional" (little-t) is used in
   the generic sense, while "Traditional" (big-T) is used to refer to
   UTJ. "Masorti" is used to the Conservative Movement in Israel and
   Europe.
   
   The following are some of the major divisions within Orthodoxy:
   
   "Centrist/modern/cosmopolitan" (colloquially [sometimes pejorative,
   sometimes affectionate] "kipa sruga" [crocheted skull cap]) Orthodox
   usually mean an Orthodoxy which approves of many aspects of secular
   culture, especially secular education, in addition to traditional
   Torah study. They tend to be Zionist. The precise term depends on the
   speaker - R' Norman Lamm uses "centrist," R' Shlomo Riskin uses
   "cosmopolitan" and R' Emmanuel Rackman uses "modern." The Union of
   Orthodox Jewish Congregations, Yeshiva University, and the Rabbinical
   Council of America in some sense represents this group. In Israel, the
   Mizrachi organization is a well-known representative.
   
   Some of the Liberal Orthodox/Open Orthodox/Modern Orthodox groups
   include:
     * Edah ([5]http://www.edah.org/); 47 West 34th Street, Suite 700;
       New York, NY 10001; (212) 244-7501; Fax: (212) 244-7855.
     * OzVe Shalom-Netivot Shalom (Israel).
       ([6]http://www.ariga.com/ozveshalom/)
     * The Shalom Hartman Institute (Israel).
       ([7]http://www.jajz-ed.org.il/hartman/) 12 G'dalyahu Alon St.,
       Jerusalem, Israel Tel: 02-5675320 FAX: 02-5611913 E-Mail:
       [8]shi@shi.org.il
     * Meimad (Israel). ([9]http://www.meimad.org.il/)
     * The Orthodox Caucus. ([10]http://www.orthodoxcaucus.org/)
     * Jewish Orthodox Feminists Alliance ([11]http://www.jofa.org/)
       
   Modern/Centrist Orthodox groups include the following:
     * The Union for Orthodox Congregations (OU) and the Rabbinical
       Council of America (RCA). [12]http://www.ou.org
     * The National Council for Young Israel, and the Council of Young
       Israel Rabbis. [13]http://youngisrael.org/
     * The United Synagogue of England.
       [14]http://www.brijnet.org/us/index.htm
       
   "Yeshivish" (colloquially, [sometimes pejorative, sometimes
   affectionate] "black hat" or "black") suggests an Orthodox outlook in
   which the focus of life is Torah study, as is done in Lithuanian-style
   Yeshivos. Secular culture is either tolerated or criticized for its
   corrupting influences. This group tends to be "non-Zionist" in the
   sense that they love the land of Israel and its holiness (many spend
   years in Israel for Torah study), but are unenthusiastic about secular
   Zionism and Israeli secular culture. In America, Agudah Yisroel is
   yeshivish. In Israel, Agudah Yisroel is chassidic, and Degel haTorah
   is yeshivish. This is partially because in America, the Agudah is a
   communal organization that runs a number of charitable, humaniterean
   and outreach projects and lobbies and advocates for the rights of
   Torah-observant Jews and to protect and strengthen Torah observance.
   In Israel, on the other hand, 'Agudath Israel' is a political party
   that holds seats in the parliament. The Shas contingency are generally
   considered to be in the 'Charedei' camp.
   
   Some examples of such Orthodox groups include the following:
     * The Rabbinical Alliance of the Commonwealth of Independent States
       (One of the rabbinic organizations in the former Soviet Union)
       [15]http://www.fjc.ru/alliance.htm.
     * The Chief Rabbinate of Israel
       [16]http://www.israel-mfa.gov.il/gov/relaffs.html
     * Agudath Israel of America; 84 William St., New York, NY 10038;
       (212) 797-9000
     * Agudath HaRabonim - The Union of Orthodox Rabbis Of The United
       States and Canada, 235 East Broadway, New York, NY 10002; (212)
       964-6337, (212) 964-6338
       
   The Chassidic style of Orthodox Judaism is described in [17]a later
   section.
   
   In Israel, the "Dati/Chareidi" distinction is more a matter of
   attitude towards Zionism than of political affiliation or religious
   views. The Dati tend to be more supportive of Zionism, with the
   Chareidi not having much belief in the modern Jewish state. Please
   note that these are general positions; individual members may hold
   different views and your milage may vary. Note that there are lots of
   debates over these classifications, so nothing here is cast in stone.
   
   Some other useful resources to explore the wide variety of Orthodox
   Judaism include:
     * Prof. Eli Segal's [18]"Varieties of Orthodox Judaism"
       (http://www.acs.ucalgary.ca/~elsegal/363_Transp/08_Orthodoxy.html)
       . This web page contains detailed entries on: Hasidism, The
       Opposition to Hasidism: Misnagdim, Rabbi Samson Raphael Hirsch and
       Neo-Orthodoxy, Lithuanian Hasidism: Chabad Lubavitch, The
       Lithuanian Yeshivahs, Rabbi Israel Salanter and the Musar
       (Ethical) Movement, The Aguddat Israel Movement, Orthodox Zionism,
       American Centrist/Modern Orthodoxy, Orthodox Anti-Zionism: Naturei
       Karta, Rabbi Eliezer Shach and Lithuanian Anti-Zionism, Sepharadic
       Orthodox Movements, and Messianic Orthodoxy: Gush Emunim.