What's the definition of fear?
Fear is an emotional response to threats and dangers. The key term here is emotional. It's in our DNA as a survival mechanism that triggers a response to a particular stimulus, like pain. It came in handy when we were trying to make sure we didn't get eaten by lions or plucked from the sky by pterodactyls, if you're one of those "man and dinosaur walked the earth at the same time" folks.
Fear is different than anxiety, which, as anyone who has ever had a panic attack can tell you, is an emotional response that occurs without any real danger being present. We work ourselves up to believe the threat is real, but it isn't. Our reaction, though, is all too real.