Anger is often misunderstood, because what we assume to be its manifestation might not really a true reflection of that emotion. To be sure, there are often times where a reaction could be rightly read as anger, and it is prompted by an event or experience for which anger is fully warranted. For instance, were I to suddenly walk across my office floor and kick a client in the shin, beyond feelings of surprise and pain, they would predictably experience anger and direct it my way. We might refer to this as a "primary emotion", meaning that this anger is truly what we feel; it's what's really going on inside of us.
However, for various reasons, we will sometimes exchange a primary emotion for a "secondary emotion", that is, a manifestation of feeling that serves to replace the real (primary) emotion that is overlooked or denied/disconnected. In events such as these, a person feeling an authentic fear might be inclined to show another emotion instead, if for instance, they had grown up in a family environment where expressing fear was ridiculed as a sign of weakness. The point is that people will often be showing anger - and to the best of their knowledge, be feeling this on the inside - when in truth, they are actually really experiencing a different emotion but not in touch with it. And as mentioned above, these misinterpretations understandably leave people feeling misunderstood.
While anger is certainly more complex and variable than is summarized here, and additional factors such as stress, families of origin influences, systems theory, and social learning theory all require sufficient consideration in understanding a person's angry traits or tendencies, the constructs of primary and secondary emotions are key to my approach when working with clients seeking anger management.