"Anti-Zionism" is a sub-set of "Anti-Semitism" (or "Jew hatred") in that Anti-Zionism seeks to deny the Jewish people but only the Jewish people, the natural right of national self-determination in their ancestral homeland. Rather than simply being opposed to all Jewish activities, Anti-Zionists seek to suppress political expression by Jews. In recent years, "Zionist" is used as a politically acceptable slur directed to a Jewish person.
Of course we all know that when they say, "Anti-Zionist", it really means "Anti-Jew. "Anti-Zionism" is simply cover for "Palestinianism."