In general, stress is a part of everyday life and a normal reaction to a situation when you feel under pressure. Stress can be due to external factors affecting our lives or can be internal such as irrational thinking.
Anxiety, however, is still having those feelings of stress long after the actual offending event has passed. This constant feeling of being stressed, even though there no longer exists an imminent stressful situation you have to deal with, is what is classed as anxiety.
In the worst case if anxious feelings are not managed they could lead to depression.
No. Stress is the cause, anxiety is the result. - Blu