When depression and anxiety appear together, either condition can be the cause or the result of the other. Someone who is depressed, as an example, can become anxious and this may be especially true as a depressed conditions lingers. An anxious person can become withdrawn or begin to feel overwhelmed by their condition, an outlook that may bring about a depressed state. If there is a more likely scenario for a lead in between the two conditions, it may be anxiety leading to depression.
The depressed state presents, usually, a reduction in one's physical expression. Depressed people are often, though not always, emotionally down and physically listless. The depressed state is not classically a state of displaced energy, a description that matches anxiety quite well. Someone depressed who suddenly displays anxiety may in fact be displaying symptoms of bipolar disorder. Bipolar disorder is marked by lethargic depression swinging to agitation, but the agitation in bipolar disorder is mania, not anxiety. The manic state typically presents extroverted, extreme, and often exceptionally strange behavior. People with anxiety aren't typically extroverted, and don't typically display especially unusual behavior.
People with chronic anxiety are uptight certainly, and this uptight and upset can become an enormous drain on the chronically anxious person. After a time of feeling chronically anxious, a person can become physically and emotionally run down, and depression may set in additional to the anxiety already present. People who have anxiety also tend to become withdrawn, or to self-medicate using alcohol or drugs, and both of these coping methods can and do lead to significant depression.
As with all human conditions, emotional disorders are not uniform but do have similarities. An anxious person need not develop depression, while someone with depression may go on to develop an anxious state that is not in fact symptomatic of bipolar disorder. If there is an important reflection to keep in mind it's that a case of depression or anxiety does not automatically discount the possibility of some other emotional dysfunction also being present. Different emotional disorders can be present at the same time.