Sh'ma Yisrael Adonai Elohaynu Adonai Echad
Hear, Israel, the Lord is our God, the Lord is One.
What is the Difference Between Judaism and Zionism?
By Yochanan ben Avraham (John of AllFaith) 4.6.10
This is an important question!
The short answer:
Judaism is a religion
Zionism is a political doctrine.
Judaism:
Judaism is the religion established by the God of Abraham, Isaac and Jacob through Moses.
HaShem ("the NAME" -- the One God) revealed His Torah (Laws and Teachings) to Moses and codified His eternal covenant with the Jewish people at Mount Sinai following the Exodus from Egypt. Unlike most religions there is also a hereditary aspect in that everyone whose mother is Jewish is automatically accepted as Jewish by Rabbinical Judaism (the largest branch of Judaism by far -- composed of the Orthodox, Reformed, Conservative and Reconstructionist movements/denominations). These are the spiritual successors to the P'rushim or Pharisees.
There is also the much smaller Karaite Jewish movement that follows a paternal membership and has certain unique views (not accepting the Oral Torah as divinely inspired, differences on Shabbat observances and so on). These are the spiritual successors of the Tz'dukim or Sadducee sect, although less directly.
Zionism:
Zionism is the belief that Zion (Mount Moria/the Temple Mount and the City of Jerusalem) is the eternal homeland and capital of the Jewish people and their rightful possession.
Early modern Zionists like Judah ben Solomon Chai Alkalai (1798 – October 1878), Rabbi Zvi Hirsh Kalischer (March 24, 1795 - October 16, 1874), Theodore Herzl (May 2, 1860 — July 3, 1904), Ze'ev Jabotinsky (October 18, 1880 - August 4, 1940) and others added their own flavors, but essentially this is what Zionism is. It is the living commitment of the Jewish people to their homeland that is manifested in the ancient prayer: Next year in Jerusalem!
While most Jews are Zionists some are not and many Zionists (including me) are not Jewish at all.
Not all Zionists (of whatever religion or sect) are religious nor base their Zionist views on religious beliefs. Some are Zionists because of religion, some out a sense of ethnic pride and dedication, some as a matter of civil and human rights, some out of political expediency or for other reasons.