The problem is that the lines between many of these words are confusing and often intentionally blurred by people on various sides.
While the definition of Semite includes Arabs and other people[1], anti-Semite is specifically defined as hostility towards Jews.[2]
Also not all Jews are Israelis, not all Israelis are Jews, not all Israelis or Jews are Zionists, and not all Zionists are Jews or Israelis.
It therefore is anti-Semitic when Jews are blamed for the actions of either Israelis or Zionists the same way it would be anti-Muslim to blame any random Muslim person for the actions of the Saudi government or any other specific group of Arab people.
[1] - https://www.merriam-webster.com/dictionary/Semite
[2] - https://www.merriam-webster.com/dictionary/anti-Semite