Denying Israel's right to exist is not anti-Semitism in and of itself. There's only one country that people want to deny the right to exist, and that's Israel (the only Jewish country in the world). The whole movement stems from anti-Semitism, but that doesn't mean that the people who believe it today, when the movement has been established for such a long time, are anti-Semitic. They perhaps don't see the origins of what they believe, but no, being anti-Israel is not the same as being anti-Semitic.
That being said, a lot of people are both, and it's not hard to see. Calling Jews "dirty Zionists" or something of the sort is a pretty clear indicator. Assuming all Jews are Zionists and blaming us for the actions of the Israeli government is something that you wouldn't do anywhere else. I don't blame all British people for Cameron or all Americans for Bush. So why, when the Jewish population around the world is so liberal, do you blame us for the conservative Israeli government's actions? I'm American. I support Israel's right to exist. I condemn many actions that Bibi especially has taken. I condemn just about everything Hamas has ever done. It's a balanced view that comes along with the so-called crazy notion that a country that's been under attack since day one shouldn't have its legal existence stripped from it.