How many variations of judaism exist today?

Answer 1

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.

Answer 2

All Jews have the same Torah.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.See also the Related Links.

Link: Types of Jews

Link: What is life like for religious Jews

Link: Modern challenges for observant Jews