Thank you for writing to Jewish Values Online. I am afraid that I find your question confusing. It would all depend on to whom you addressed your question, and in what context.
At one level, there is only one kind of Judaism. One either is a Jew or is not.
At a different level, there are multiple varieties of how Judaism is practiced. In this, one might talk about Conservative, Orthodox, Reform, Reconstructioninst, Renewal, Habad/Lubavitch, Satmar, and other groupings or segments of the Jewish world.
At yet another level, one could discuss Secular, Modern, Religious, Observant, Ethnic, Cultural, Social, Ethical, Artistic, Literary, and still more types of Jews and Judaisms in the world.
And of course there are Traditional, Progressive, Liberal, and Feminist Judaisms.
Most confusing of all is that all of these can exist in almost any combination and permutation, so one could meet a person that said that he/she was a Modern Reconstructionist Traditional Religious Observant Cultural Social Feminist and Ethnic Jew; to pick just one example.
So the answer is either one, multiple, or many, depending on what you mean.
If you would like to clarify and re-submit your question with more details, we can try to answer what it is you are specifically asking. Alternatively, you might find that there are many other sources on the web that already try to address the question you mean to ask.
Answered by: Rabbi Joseph Blair