Depression is certainly well known, if not actually understood. Many people refer to feeling sad or disappointed as "being depressed". This is a factually incorrect description. Depression is, in part, a chronic change in one's mood, outlook, or behavior. Normal sadness and disappointment don't linger on for weeks at a time.
Bipolar Disorder is a swing between feeling euphoric mania, and major depression. Bipolar Disorder can have a severe impact on the lives of people inflicted with it, as the euphoric mania stage sometimes results in excessive, irresponsible behavior -- spending a great deal of money unwisely, for instance, or inappropriately interjecting oneself into certain situations -- while the major depressive stage can leave a person almost completely incapacitated, and sometimes leads to a suicide attempt. In almost all cases of Bipolar Disorder, a mood stabilizing medication must be used for successful treatment to take place. Fortunately, most people with Bipolar Disorder do respond to appropriate treatment, and as long as they remain in treatment, those with Bipolar Disorder can often lead normal lives.
Having anxiety is quite a different scenario than having Bipolar Disorder. Anxiety is, generally speaking, feeling emotionally overwhelmed and/or extremely fearful, be it most of the time, or only in certain situations. The person with anxiety may feel as though they aren't in control, but an anxious person typically isn't going to engage in public displays of irrational or unreasonable behavior like someone with Bipolar Disorder may. While the person with anxiety often fears that they don't have control over themselves, the person with Bipolar Disorder usually has no such concerns; in fact, the person with Bipolar Disorder typically considers their behavior to be completely normal. One of the telltale signs of anxiety is a fear of losing control over one's behavior, or of "going crazy": many anxious people, in fact, have a deep fear of becoming mentally ill. Interestingly enough, this fear of becoming mentally ill is typically an indication that one is not mentally ill at all, as most people who are truly mentally ill consider themselves to be normal and healthy, and may even react hostilely to anyone suggesting otherwise.
While using the term mood disorder when one really means anxiety may just be a case of semantics, it is important to differentiate between various emotional and psychological conditions, if for no other reason than to ensure proper treatment.