The core difference between Judaism and Zionism is that the former refers to the Jewish religion and traditions, whereas the latter is a political ideology.
Another really notable difference between Judaism and Zionism is that the former is a religion that describes the values, rites and beliefs of the Jewish people, whereas the latter is a political ideology that insists on the right of the Jewish people to have their own political state in the territory where they lived in Biblical times, i.e. the Promised land. Zionism is campaign for the Jewish people to relocate to their ancestral homeland, so that they no longer have to worry about the oppression and anti-Semitism that they have had to endure for centuries at the hands of other religions across the globe. The desire to feel safe and feel secure is the basic foundation of Zionism.
Judaism and Zionism differ on the issue of the State of Israel. This difference, however, is only present between the orthodox. While both Jews and Zionist believe that the Promised Land indeed belongs to them and wish to build a Jewish state on their ancestral homeland, the orthodox Jews believe that this desire will only be fulfilled after the arrival of a messiah. The Zionists, however, have decided to fight for their right to a separate homeland instead of waiting for the arrival of the messiah.
Judaism only includes the Jewish people, whereas Zionism comprise of Jews, Christians, Hindus and even Muslims. The reason for such a strong support for Zionism is based on human and civil rights. Furthermore, the mass murder of Jews (holocaust) of the Nazi Germans under the rule of Adolf Hitler has resulted in a significant population across the world realising and respecting the requirement of a separate homeland for the Jewish people.