A Semitic is anyone from the middle eastern area around Israel. Anti-semitic means you are against all of them.
Anti-zionist is against the religion of Israel.
From the Cambridge Dictionary,
"Zionism: a political movement that had as its original aim the creation of a country for Jewish people, and that now supports the state of Israel".
"Anti-semitism:the strong dislike or cruel and unfair treatment of Jewish people"
https://dictionary.cambridge.org/fr/dictionnaire/anglais/anti-semitism?q=anti-Semitism
A large number of Arabs in France are "Semites" according to your definition, but since they are so stupid, are anti-Semites, they hate the Jews even the Jews who come from North Africa and who look like them like brothers.
SACRED FIRST RUNNER-UP OF MISS FRANCE, APRIL BENAYOUM WAS THE VICTIM OF ANTI-SEMITIC COMMENTS ON TWITTER; IT'S NOT ANTI-SEMITISM IT'S ANTI-ZIONISM! SO WHY DO YOU ALWAYS CRY RACISM WHENEVER SOMEONE CRITICIZES ISLAM?