We all have fear and anxiety once in a while, which are necessary and natural reactions. There is, however, a slight difference in meaning between the two concepts. Fear is the more natural, and if you like, healthier response compared to anxiety.
Fear usually involves a concrete sense of danger. You are faced with a certain threat in the environment and have generally two choices: fight or flee. I personally prefer the second one, to escape and evade the danger. Let heroes choose the brave and valiant option of facing the threat. I would rather live a coward than die a hero. To justify my cowardice and to restore a little bit of personal dignity, part of my decision to avoid harm onto myself is the feeling of ongoing responsibility I have toward my wife and son.
On the other hand, anxiety is the feeling of fear but toward a vague object. Anxiety is the uneasy feeling, the queasy sense of danger, regardless of its validity. It is, for example, our constant fear of the dark. Of course, in evolutionary times, this had the real purpose of protecting human life because of dangerous animals lurking around. Similarly, there are certain areas in every city that one should avoid at night for security reasons. Nonetheless, to be afraid of the dark within the safe confines of one's home is rather exaggerated and not substantiated. That is the type of fear I am referring to here as anxiety.
Now I am not claiming that everybody can control these feelings of anxiety. To a certain extent, we cannot help feeling anxious, as anxiety persistently resists the arguments of logic and reason, like the anxiety over an upcoming exam or job interview, regardless of one's preparation, chances or qualifications. In other cases, it can be part of a mental disorder, such as agoraphobia, the fear of open spaces, or its confined version, claustrophobia.
The same way fear of heights means anxious feelings about being faced with heights, claustrophobia is the anxiety of being in a closed oppressive position. The odds of getting stuck in an elevator are generally not that high, compared to how many times we take the elevator in a given year. But once we have had the unfortunate experience of being stuck, it may translate into a general anxiety regarding elevators. We would rather take the stairs from then on.
In this case, the imagined fear or anxiety is greater and disproportionate in relation to the occurrence itself. People rarely die from being stuck in an elevator and sooner or later, help will come. We have then a case where our imagination adds fuel to our fear. We become terrified of the possibility of the event to the extent that we feel paralyzed. Such emotions can be observed in social or romantic situations when we feel our throat tighten and our voice falter when talking to an attractive person. We often feel threatened when faced with beauty and desirableness.
But this kind of fear does not make sense and is counterproductive and eventually nothing but a figment of one's imagination. What harm could come from such a social situation, for example? At worst, the beautiful stranger would refuse to talk to us or reject our advances, even make fun of us. The actual event is indeed half as painful as we would imagine it. Rejection, in any form and at any level, may hurt, but it is a part of life, and it is really, all things considered, not that big a deal.
In all those instances, it is imagination, not fear itself that we need to fear. Our mind distorts the information, becomes irrational and becomes stubborn and blind toward the actual facts. The true hero is not so much the person who fights the threat, but the one that goes through life with his head up high and with the confidence that fear may be partially real, but is mostly a product of the imagination.