If you mean religion:
There are several different denominations that vary by country:
- In the US/Canada, the 4 main denominations are Orthodox, Conservative, Reform, and Recontructionist.
- In the UK, the 4 main denominations are Orthodox, Masorti, Reform, and Liberal.
- In Ireland, the 2 main denominations are Orthodox and progressive.
- In Israel, the 1 main denomination is Orthodox, though the Reform movement is gaining ground there.
If you mean ethnicity, there are currently two main groups: Ashkenazic and Sefardic.
Answer 2
First of all, it should be stressed that all Jews have the same Torah.
Jews may be classed according to lifestyle, geography, or outlook.
Lifestyle:
There are Jews who are more stringent (Orthodox) or less stringent (Conservative, Reform) in their observance of the Torah's commands. Orthodox Jews believe that the Torah must be fully observed (Deuteronomy 13:5). They keep the laws of
Judaism as codified in the Shulchan Arukh (Code of Jewish Law), which lists the laws of the Torah and Talmud. Torah-study is seen as very important (Deuteronomy 5:1); and the modern world is seen as subservient to the Torah (Talmud, Nedarim 32a), not the other way around.
Other Jewish groups (Conservative, Reform) adapt, curtail or change the Torah-laws in contemporary life, to a greater or lesser degree.
Geography:
There are Ashkenazi (Western) Jews and Sephardi/Mizrahi (Eastern) Jews. In Medieval times, the Ashkenazim were in France and
Germany, the Sephardim were in pre-expulsion Spain, and the Mizrahi (Edot Hamizrach) were in
North Africa, Turkey and Iraq. (There are others too, such as Yemeni and Romaniote (Greek Jews), but the above are the largest groups.)
Outlook:
Among the religious Jewish communities, there are the Yeshiva (Litvish) community, Hassidim, and Modern Orthodox. (Hassidim are the ones who wear long frock-coats.)