That is the antisemitism. And anti-zionism IS antisemitism. The fact some anti semites are clever enough to try and hide their abhorrent racism behind word play is laughable.
And here we get the pernicious concept of the self-hating Jew.
"Anti-Zionism is hatred of Jews".
"I'm Jewish and I'm against Zionism".
"You're not a real Jew / You're a self-hating Jew / You don't count for reason X"
Or
"I'm against Zionism but I have Jewish friends / partner"
"Then you're a hypocrite because you're self-contradicting."
"???????"
Basically, saying zionism == jewish and anti-zionism == anti-jewish is just an argument by assertion that the definition is what suits you. But neither history nor general consensus support that. Not least because Zionism is a modern invention and Jewish people have been around for most of recorded history.