Before I define the label “Orthodox”, I want to spell out what kind of entity is being labeled.
The Enlightenment and the fall of the ghetto walls created a religious crisis for Ashkenazic Jewry. First for those in Western Europe, but the development does reach Eastern Europe over the course of the next several decades. Until then, for most people Jewish observance and belief were not subject to conscious decision. This is the lifestyle of the Jew. Each area really only had one, they didn’t differ all that much.
Then the Enlightenment gave Jews a choice. People needed a reason to stick to Judaism. An ideal to aspire to. And that led to the rise of movements. Some movements, like German Reform, responded to the new opportunity by not insisting on those qualities of Judaism we call Orthodoxy. Chassidus was a different kind of early response; to give the people in the field that ideal, a way of being passionate about one’s Judaism that would make it more appealing than the newly offered other choice — assimilation. (In fact, it was not 100% clear in the 2nd generation which way chassidus would end up going. The Tzemach Tzedeq, the 3rd Lubavitch Rebbe, allegedly credited the Vilna Gaon and the Misnagdic opposition to weeding out the more avante-gard and anti-nomian splinters of the Chassidic movement.)
In Hungary, the Chasam Sofer’s response was a counter-reaction, with the slogan “Chadah assur min haTorah — the new is prohibited by the Torah”.
And similarly, Germany produced two very different forms of Neo-Orthodoxy — one by R’ SR Hirsch, the other based in Berlin. They did not mingle socially, and were in fact recognized by the Prussian Government as members of separate religions. (The Berlin form being unified with the non-O Jews, whereas Rav Hirsch’s community “walked out”, forming the Austritt community.)
The Vilna Gaon’s tradition evolved into the Yeshiva and Mussar Movements.
Meanwhile, the more modern elements of East European Jewry embraced the new wisdom calling itself the Haskalah (Enlightenment, in Hebrew) and studied Judaism from a more academic and scientific perspective. In their hopes to modernize the community as a whole, they ended up undermining the more traditional movements. America developed its own version of Reform. Back in Europe, Neolog gained ground.
Then we had Conservative, Modern Orthodoxy, Religious Zionism, the American and Israeli Yeshiva Movements (trying to recreate the Lithuanian original, but not quite ideologically identical), the rebuilding of post-War chassidus, etc…
All this went on among Ashkenazim. There was no similar culture shock in the rest of the Jewish world, so there was no similar rise of Isms. But when Ashkenazi, Sepharadic, Ottoman and Yemenite Jewish communities met, primarily in Israel, those other communities saw Orthodoxy as having the nearest equivalent of their One Jewish Lifestyle version of Judaism. And so the Chakham Baqshi, the Chief Rabbi of Palestine under the Ottoman Empire worked together with the Orthodox rabbinate, not the other movements. Orthodoxy isn’t a property these Ashkenazi movements mutually created, it is a property they preserved.
So, Orthodoxy is less a movement as a set of movements, or at least the property they all share in common. Unlike Reform or Conservative Judaism, there is no defining group of ordination schools, that we can define “Orthodox ordination” by listing a handful of institutions, no synagogue umbrella, and most definitely O synagogues don’t belong to any umbrella.
The definition of that property, Orthodoxy, admittedly has yet to be addressed. To segue into that… The American Conservative movement is a good example to use for illustration. JTS, now JTSA, the Conservative rabbinical academy, was founded by the same people who had started the Orthodox Union. After the Great Depression, when charity money was at a premium, there was even discussion of a merger between Yeshiva College (now: Yeshiva University) and JTS. But now, no one would consider JTS and Conservative Judaism as an Orthodox Movement.
What changed? Three things really:
1- The negotiations with YU fell apart largely over a single person — Mordechai Kaplan, who later leaves C to found Reconstructionism. His philosophy was just too heretical (by Orthodox standards) to be acceptable in a religious teacher in an O institution.
2- The driving responsum, allowing people who couldn’t otherwise reach services to drive to them on Shabbos, was a leniency that the Orthodox halachic process couldn’t countenance.
C developed from the Breslau Historical School (many of whom were considered O) who saw the sages of the mishnah and the talmuds in their historical context, and thought that this kind of analysis is important to understanding the halakhah. And once one accepts that halakhah has always been malleable enough to be used by the rabbinate for what they considered noble social and political ends, it is natural for contemporary rabbis to do the same.
3- It became the norm in JTS to teach Document Hypothesis, the idea that the Torah was revealed piecemeal over the course of generations, rather than a literal revelation to Moshe in the Sinai desert. (With a possible exception of the transmission of the last eight verses and other nits one can pick.)
Whereas within Orthodoxy, acceptable beliefs are presumed to be explicable in some way as loosely conforming to the 13 Articles of Faith. Likely not the Rambam’s original, but somehow affirming the versions in the siddur — Ani Maamin and Yigdal.
In other words. they disagreed on Who, What and Why.
Meanwhile, within Orthodoxy, Rav Moshe Feinstein, Rav Menshe Klein, an Rav Ovadia Yosef (eg) came from very different communities, had significantly different worldviews, and also disagreed on practical rulings. But they agreed on certain basics of the faith, and enough about the process of how to come up with a ruling, to mutually acknowledge and respect each other’s positions as valid.