Although fear has been classified as an emotion by psychologists, it is a very basic human emotion and can be almost considered as a simple feeling. In fact if emotions comprise of feelings and bodily reactions, then fear would be the basic feeling component of anxiety or phobias as has been explained in the psychology of emotions. I prefer the use of fear as feeling rather than as an emotion and to explain this, it is important to distinguish between feelings and emotions in psychology. As of now this distinction is blurred and psychologists do not distinguish between feeling and emotion extensively.
Emotions are complex mental and physical processes as emotions involve feelings which are mental or psychological components and bodily reactions which are physical reactions. Thus feeling is an essential part of emotion. The simple feeling is purely psychological and does not involve bodily reactions and that is how fear which may or may not involve bodily reactions could be both a feeling and an emotion. For example fear of a student at the examination centre would be accompanied by bodily reactions such as rapid heart beats or flushed face, dilated pupils and so on. Although fear which could be a feeling component may be very simple and generalized and could be even unconscious without the presence of bodily reaction, although not as intense as anxiety which necessarily involves bodily reactions. Thus perhaps you are on stage and performing a play, you may not directly sense any bodily reaction and could be calm and normal but you may still harbour a feeling of fear as in some sort of uneasiness.
Fear could thus be both a feeling and an emotion yet fear as an entirely subjective or mental feeling component would be difficult to detect as it would not be accompanied by visible or noticeable physical reactions as in fear as an emotion. Anxiety on the other hand is considered a distinct internalized emotion as it arises internally from a perceived threat rather than fear which is due to external stimuli. Fear could be defined as an externalized emotion or feeling which may or may not be accompanied by bodily reactions and fear could be conscious or unconscious.
A psychology of fear would distinguish fear as an emotion and fear as a feeling, fear as conscious and fear as unconscious as well as fear with bodily reactions and fear without bodily reactions and fear in anxiety and fear in phobias. It would be important to understand why fear occurs and what are the bodily reactions when fear is a strong conscious emotion and how this differs from fear as a feeling which may not have bodily reactions and could be conscious but would more likely would be unconscious.
Say for example you have an unconscious fear of old haunted dilapidated houses and you repeatedly dream of events in such houses, the dream itself could cause some bodily reactions but it is not apparently obvious that the fear is causing the bodily reaction. So in this case, the fear itself is simply unconscious and a feeling which manifests in dreams and the dreams are associated with bodily reactions and not the fear. So here fear is a feeling rather than an emotion. Some psychologists would however argue that this "fear' could simply be an undefined anxiety but since the psychologists would also identify the cause of the fear (or anxiety as they would say) which is a fear of haunted houses, this is still an externalized fear and not internalized anxiety. Fear is thus externalized whether it is a feeling or an emotion.
The distinction between feelings and emotions are like trying to distinguish between meteoroids and asteroids in outer space and the distinction would require very detailed analysis of the layers of the mind. At this point we do not have sufficient frameworks or scientific evidence that would help to make this distinction easy. Modern studies in consciousness have focused on this problem of feeling. As Thomas Nagel highlighted in his very famous paper "What is it like to be Bat?' this subjective feeling of "what it is like to be' is very important. With the study of consciousness, the subjective aspects of emotions are all important and although hardcore physicalists who believe that our minds are nothing but neuronal firings would ignore that an emotion would have a feeling aspect, studies in consciousness have proved that feeling or the subjective aspect of being is the core of being human.
However the topic being the psychology of fear, it is essential to understand why fear happens and what would be the therapeutic directions for fear. Fear could be characterized as a general unconscious feeling of unpleasantness or could be more complex emotion such as anxiety and externalized fear. Fear could also be phobias which are persistent pathological fears directed towards specific objects and situations. Phobias could be of spiders or heights and these are exaggerated or extreme forms of fear with severe bodily reactions, almost bordering on paranoid reactions. Fear could thus be revealed as severe emotions with bodily reactions, and can be manifested as anxiety or phobia, fear could also be a general feeling. In order to understand why fear happens we distinguish the types of fear:
Fear as Emotions - Fear when accompanied by bodily reactions would signify strong emotional response to a situation or an object or event. Since fear is internalized, fear would naturally begin with a feeling or a subjective component. This means the individual would first "feel' afraid of the situation and then react to it. Such fear in which the individual is conscious of the emotion and reacts strongly to it is generally an emotional response and this sort of fear is thus manifested as a strong emotion.
Fear as Feeling - Fear could however be simply manifested as a subjective feeling, a sense of uneasiness or unconscious perception of some sort of danger or threat that may not evoke strong bodily reactions. Fear as feeling is thus unconsciously released in dreams, slips of tongue, lapses of attention etc.
Fearin Anxiety - Fear as a feeling could also be the subjective basis of anxiety as when internalized and even unexplained anxiety has a general feeling of fear. Anxiety thus also begins with a fear but this could be largely unconscious, internalized and more generalized. But anxiety has distinct bodily reactions and that is how anxiety differs from fear as a feeling.
Fear in Phobias - Fearin phobias consist of persistent pathological emotional response towards specific objects or events. The difference between anxiety and phobia is that phobias are always externalized whereas anxiety is internalized and fear again being externalized as an emotion or internalized as a feeling would be a part of both anxiety and phobias. However phobias are not emotions but pathological responses consisting of fear as a complex emotion and bodily reaction. Since phobias are compositions of emotions and strong reactions, the reactions are expressed in exaggerated forms in phobias so individuals with phobias would react in extreme ways and could develop a state of panic especially due to the extreme and uncontrollable bodily reactions.
In therapeutic treatment of psychology it will be necessary to understand the origin of fear and this could be done with neurological studies and studies of bodily reactions and mental states. Fear as simple feelings or complex emotional responses should be identified in specific situations and extensive fear could be studied in anxiety and phobia.