DaMoshe, in the United States the Conservative movement was an offshoot of the MO movement. As earlier mentioned, many of the same rabbis that founded the Orthodox Union (OU) also founded the Conservative Jewish Theological Seminary.
So-called Chareidim never existed as a term until the MO made their seperatist movement within Orthodoxy. After the MO came into existence, the traditional Orthodox who never left or changed got their moniker of Chareidim, a term coined by outsiders. Chareidim are simply what was originally called Orthodox, just like the Orthodox are simply what was called Judaism before the breakaway Reform movement came about. The name Orthodox was also imposed on us by the non-Orthodox.