Stress is mainly focused on external pressures that we are aware of, for example, a tight deadline for an assignment or having an argument with a friend. It is best to tackle these head on, and once the problem is resolved the stress typically disappears. Stress is like a muscle, when you find ways to manage the stress and practice using the muscle, you are able to handle more the next time.
Anxiety is focused on internal pressures that are a reaction to stress, and sometimes there is not a specific cause. We are not always aware of these problems, and are not as easy to figure out. Anxiety is characterized by feelings of worry and tension, and people may avoid certain situations because of these feelings. Build up of smaller stressors and big events can trigger anxiety.
