Any one who is born of a Jewish mother is traditionally understood to be Jewish. There are though different types of Judaism practiced which are:
Orthodox – Orthadox Jews believe the Torah and the Talmud Contain the actual words of God which must be Applied in all circumstances.
Orthodoxy also includes:
Hasidim – Followers of the teaching of Israel Ben Eliezer
Haredim – sometimes refered to as Ultra-orthadox
Progressive – They believe in the divine inspiration of the Torah but since it was recorded by humans at a certain point of time in history, it then becomes necessary to
reinterpret the words in the context of the times you are living in.
Reform Judaism – established in early 19thCentury
Liberal Judaism – originally an offshoot of Reform