Stress is a natural response to factors in the environment. Stress motivates us to change things in our environment. There is actually an optimal level of stress to be functional- too much stress is bad for you, but no stress at all means you never do anything.
When we are experiencing too much stress, and find ourselves unable to modify the stressors in our environment, we may experience anxiety or depression.
So stress is a response to stressors in your social or physical environment, and anxiety is a response to unresolved stress.
Each individual has a different level of vulnerability to stress, and a different "stress/vulnerability threshold". Once the amount of stress exceeds their personal threshold, they will typically exhibit symptoms such as anxiety;
Anxiety is seen as a disorder if it persists when the stressors are removed. Chronic anxiety may be caused by internal physical or psychological factors, rather than external environmental ones.
Of course sometimes we can't remove or move away from the things that stress us. While symptoms like chronic anxiety and depression are listed as mental disorders, there are life circumstances in which if you are not depressed or anxious there is something wrong with you- homelessness, domestic abuse etc. In such circumstances treating the symptoms is not usually of much use, without attention to reducing the chronic stressors that cause them...
First of all, anxiety is an emotional response to external stimuli (e.g. stressors) as well as internal stimuli (e.g. images, thoughts, needs) and sometimes it is contrasted with fear, referred to the response only to the external stimulus. For example, taking the experiential approach, the anxiety may motivate to find out what important values or resources have been threatened and may help to reorganise them. I just wanted to highlight the "salutogenetic" value of the anxiety but most forms of anxiety are not adaptive and are associated with neurotic features, dissociative and dismorphic disorders, stress related disorders and other forms of anxiety disorders.