There are as many kinds of Jews as there are individuals. Originally, there were 12 tribes, but today, almost all Jews are of the tribes of Judah, Levi or Benjamin. Jews are also sometimes grouped ethnically: those originating from central and eastern Europe are called Ashkenazim, while the descendants of the exiles from Spain are called Sephardim. Often, all Jews from Arab lands are called Sephardim.
Grouping by level of practice, affiliation, or ideology is much more difficult, and often artificial and unhelpful.