Since the early 1800’s, after the French Revolution and the European “Enlightenment”, when Europeans started going away from Religion and towards science, there has developed many denominations in Judaism (much the same as Protestant Christianity). Prior to 1800, there was only Orthodox Torah Judaism. Then, amongst mostly German Jews, there developed Reform Judaism. This was an attempt to rid Judaism of anything distinctly Jewish (such as Circumcision, Keeping the Sabbath, Keeping Kosher, etc.)… It was an assimilationist movement aimed at becoming more part of mainstream German culture and more like their Christian neighbors. This is currently the biggest movement in the USA.
These are the main denominations (as of me writing this document). #2-#7 is listed in order of observance/belief…
Chasidic Orthodox (also called Ultra-Orthodox or Haredi)… due to their Eastern European style dress and long Payot (side-curls).
Orthodox (also called Haredi, Misnagdim, Litvish, Litvack, Yeshivaish, Torah Judaism, etc.)
Modern Orthodox (most are Religious Zionists)
Secular (not an official movement)
Socialist Zionist (also called the Labor Party in Israel)
Movements # 1, 4, 5, 6, 7, and 9 are mainly Ashkenazi (European Jewish) movements that started either in Europe or the USA. Traditionally Sephardic or Mizrahi Jews were just Orthodox when living in their respective Muslim countries. Since moving to Israel (as there are not many in the USA), some Sephardim/Mizrahim have become Modern Orthodox (such as the Religious Zionists) or completely Secular.
First, I will mention what Orthodox Judaism is as that is the original Rabbinic Judaism, dating back 2000 years since the destruction of the Temple in Jerusalem by the Romans. Rabbinic Judaism, it should be noted is quite different than Temple Judaism, where worship was centered around the Kohens (Priests) and the Levites in the Temple and on Animal Sacrifice. Rabbinic Judaism is centered around the Talmud, which is an Oral Tradition passed on from Moses in 1300 BCE to the Rabbis of the 2nd Century CE which is used to explain the Torah (the first 5 books of the Bible and its 613 laws). Roughly half of the 613 laws cannot be followed unless the Temple in Jerusalem is standing and you live in the Land of Israel. But of the remaining 300 or so… these are some examples of laws that Orthodox Jews would keep…
To keep the laws of the Sabbath (not driving, not turning on or off the lights, not working, creating a fire)
To keep the laws of the Festivals (Pesach, Shavuoth, Rosh Hashanah, Yom Kippur, Sukkot, etc.)
To keep the dietary laws (inside and outside of the home)… no pork, shellfish, camel, mixing milk and meat, etc.
Must have different plates, utensils, pots and pans, for Dairy, Meat, and Passover Meals.
Women wear skirts below the knee (some groups say to the ankle) and no pants at all.
Married women must cover their hair (different groups differ based on what they can use such as a scarf, a hat, a wig)
Men must pray 3x a day (Shacharit, Mincha, and Maariv).
Men must wear Tzitzit every day all day.
Men must put on Tefillin (phylacteries) every day except for Sabbath and Festivals.
Men must wear a Kippah (skullcap) all of the time.
Must put a Mezuzah at all doorposts (including every doorway inside the home).
Most, but not all, will forbid the shaving of the beard.
Men and Women sit separately in the Synagogue.
The difference between the Orthodox and the Chasidim, is that the Chasidim follow the teachings of the 18th Century Baal Shem Tov and their respective Rebbe (a Torah Scholar descending from whatever city their ancestors come from in Eastern Europe). The Chasidim traditionally put more emphasis on Kabbalistic (Mystical) teachings and Joy in Worship (Singing and Dancing,) more so than on just Yeshiva Learning and following laws (Halachah) without an emotional attachment (Immense Love) of God. They also put a lot of emphasis on learning through Storytelling. Also, they try to go beyond what is the minimum requirement. For example, instead of just having a beard and payot, they will not trim it at all, but just let it grow naturally. They also ascribe kabbalistic spiritual significances to this (long beards and payot). Many of the Chasidic Dynasties are extremely Anti-Zionist, including the largest one, the Satmar Chasidim. One of its late Rebbes, Rabbi Joel Teitelbaum, was even one of the main inspirations for the Neturei Karta.
Modern Orthodox is an attempt to reconcile following Orthodox Torah law with a more modern outlook or worldview. They will have different interpretations on laws to rationalize their modernizations. Examples include many will shave their beards with an electronic razor (not a manual razor) because it does not get quite as close. Some of the women will wear pants and some will use hats to cover their hair instead of the traditional scarf. And some may not wear a kippah while at work. A good example of Modern Orthodox (to the extent of my knowledge) is Senator Joseph Lieberman.
Conservadox is a mesh of Modern Orthodoxy with the Conservative movement. It does not follow all of the laws of Orthodoxy like keeping the Sabbath and all of the Dietary laws but is more orthodox than the conservative movement.
The Conservative movement started in the USA as a reaction to the Reform movement as being too extremely liberal and un-Jewish in their beliefs and practices. They are not Orthodox… meaning they might drive to the synagogue on the Sabbath and only keep Kosher inside the home, and do not have separate seating for men and women inside the synagogue. They do not wear Tzitzit or Tefillin. They normally will only have a mezuzah at the external entrances to their home, not every doorpost inside their home.
The Reconstructionist movement is a modern movement of the 20th century that is even further to the extreme left of Reform Judaism. For example, they deny all miracles, such as the miraculous giving of the Torah at Mt. Sinai and the Splitting of the Red Sea, the 10 plagues, etc. Many even deny the existence of God but rather put all emphasis on doing good deeds and Tikkun Olam (Repairing the World).
Lastly, the Secular are just Jews who are not associated with any of the above established movements. Most Jews in Israel are Secular as most Reform, Conservative, or Reconstructionist reside in the USA. Israel is predominately just Orthodox or Secular. Though as of recent with large migrations of Zionist Jews from the USA to Israel, these movements have recently become established in Israel.
The State of Israel and its founders were adherents to the Socialist Nationalistic philosophy of Karl Marx. The Zionists, beginning in the late 19th Century were staunchly secular, if not atheist, wanting a national home for the Jews, as an ethnic entity, having nothing to do with traditional Judaism. Their tie to the Land of Israel is based on History, not religion. Being that Israel was the national homeland for the Jews from 1300 BCE to 135 CE, it made the most sense to reestablish their homeland where their ancestors had originally lived prior to being forcibly expelled by the Roman Pagan Heathens. Until 1967, the majority of religious Jews were staunchly Anti-Zionist such as the Chofetz Chaim. There were exceptions… Rabbi Abraham Isaac Kook was a proponent of the Zionist ideology although he was extremely religious. Because many Religious Jews perceived the 1967 6-day war to be miraculous, that is what formed what is now called the ‘Religious Zionist’ Camp.