Conservadox is the term sometimes used to describe Jews whose beliefs and practices place them on the religious continuum somewhere between Conservative Judaism and Modern Orthodox Judaism. The term "Traditional" (not to be confused with the more generic term "traditional") is sometimes applied to roughly the same sector of the community.
Until the 1970s, traditional Conservative and liberal Orthodox synagogues had a substantial area of overlap, with many congregations calling themselves either Orthodox or Conservative having a similar combination of a traditional liturgy in a synagogue with mixed seating, together with traditional but lenient or lax personal observance among the membership. "Orthodox" and "Conservative" congregations could be almost identical in liturgy and practices, with a substantial interdenominational blurring. Changes in both the Conservative and Orthodox movements came to distinguish both movements more clearly, leaving an increasing gap in between.
Beginning in 1973, the Conservative movement began more actively involving women in services, and following the Conservative decision to ordain women as Rabbis in 1983 ritual egalitarianism became a distinguishing characteristic of Conservative synagogues. Although a small minority of Conservative congregations continue to maintain traditional roles, the minority became very small (10% or less) by the end of the 20th century. Throughout the 1980s and 1990s, the Conservative movement moved leftward on a variety of liturgical and social issues, shortening services, changing the traditional liturgy, developing new rules for women, and supporting liberal positions on such issues as abortion, homosexuality, public religion displays, and more. More traditional Conservative synagogues became an ever-shrinking minority.
On the Orthodox side, in the 1980s, the Orthodox Union, the principal Modern Orthodox organization of synagogues, began requiring Orthodox synagogues which had previously had mixed seating to build a mechitza with separate seating for men and women or de-affiliate, thus creating an irreconcilable physical distinction between the most liberal Orthodox-affiliated synagogues and the most traditional Conservative-affiliated ones. The Jewish Ledger reported that as of 2005, "Beth Midrash Hagadol-Beth Joseph [of Denver, CO] remains the only synagogue in the country affiliated with the Orthodox Union (OU) to have so-called 'mixed seating.'"  In addition, social trends in Judaism and in the larger society have reflected an increased rightward trend in Orthodox Judaism, including Modern Orthodox Judaism, on matters of both ritual and social outlook. The Haredi segment, which believes in separation from secular culture and in a distinction between men and women has had increasing influence. 
As a result, Conservadox Jews, who a generation ago could feel very comfortable in either an Orthodox or a Conservative setting, have become increasingly isolated from both Conservative and Orthodox Judaism as the gap between the two has widened. This trend has resulted in attempts to experiment in new organizations and liturgical styles at both the right of Conservatism and the left of Orthodoxy to appeal to this constituency.
Conservadox is largely a North American phenomenon although similar trends can be identified in Israel and Europe. Generally Judaism in Israel is more traditional and Orthodox, thus a North American entering a Conservative synagogue in Israel may perceive it to be more similar to a North American Conservadox synagogue than a North American Conservative synagogue.