This is a complex issue. In layman's term Zionism is an ideology that supports the idea of Jewish people having a homeland. Anti-Semitism deals with people who hate the Jewish people.
how they are connected:
- some say that in more modern times the term Zionism is used to cover up the real reason why nations want the Jews out of their country and that is because anti-Semitism is rising throughout Europe again and other parts of the world. So, in a round about way, they are using the positive term and feeling towards the Jewish people, Zionism, to cover up the negative term and feeling towards the Jewish, which is anti-Semitism. Does that make sense?
Hopefully I helped and good luck.