There are certainly some theoretical differences, and some undeniable differences (Neturei Karta members may be bigoted, hateful, publicity seeking morons but it would be hard to characterize them as anti-semitic)
But for the majority of ani-Zionists there is little question that they are really anti-semitic, or self-hating Jews. Whether it makes sense to accuse them of Jew-hatred based purely on their anti-Zionist statements is a different question.
There are a few good "acid tests" to distinguish between legitimate criticism of Israel or Zionism and old fashioned bigotry against Jews. One of the better definitions comes from Natan Sharansky.
He calls it the "3D" test:
- Demonization - "When the Jewish state is being demonized; when Israel's actions are blown out of all sensible proportion; when comparisons are made between Israelis and Nazis and between Palestinian refugee camps and Auschwitz - this is anti- Semitism, not legitimate criticism of Israel."
- Double Standards - "When criticism of Israel is applied selectively; when Israel is singled out by the United Nations for human rights abuses while the behavior of known and major abusers, such as China, Iran, Cuba, and Syria, is ignored; when Israel's Magen David Adom, alone among the world's ambulance services, is denied admission to the International Red Cross - this is anti-Semitism."
- Delegitimization - "When Israel's fundamental right to exist is denied - alone among all peoples in the world - this too is anti-Semitism."
There may be another reason for some of today's irrational anti-Zionism.
One other great hatred that exists in the world today that is socially acceptable is the hatred of America. As the only superpower, as well as the major economic driving force, America is the object of intense envy that manifests itself as hate. Just as in the case of Israel, the United States' very existence and success is an implicit indictment of others - in America's case, it shows the impotence of Old Europe, in Israel's case, it shows the shortcomings of her neighbors.
In either case, some of the hatred of Israel may be because it is such a staunch friend and ally of hated America. It is probably not nearly as much of a factor as old-fashioned Jew-hatred, but it is a component that may be used to differentiate between some Israel-bashers and anti-semites. It may make more sense to say that French anti-Zionism is more a consequence of French jealousy of America than innate Jew-hatred.
At any rate, Judeopundit's main point that anti-Zionism is no less bigoted than anti-semitism is well taken and worth repeating.