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From these sources (1, 2, 3) I have figured out that anxiety and stressfulness are generally defined as:
Anxiety - Prone to have generalized anxiety, panic, specific phobias, worry as well as feeling tension, nerviousness.
Stressfulness - Feeling helpless, overwhelmed under stress, pressure or when facing emergency situations.
But isn't feeling helpless and overwhelmed cause you to feel anxious? And isn't feeling of helplessness and overwhelmed basically comes from anxiety? When I feel overwhelmed, it basically means that I am very anxious at the moment.
Another definition (4) might be that stressfulness is a proclivity to feeling panic. But isn't panic is just a final stage of being anxious?
What is the difference between anxiety and stressfulness?
Your question indicates that your research indicates a close association between stress and anxiety. I've tried a few different approaches to separating these terms but with limited success. Investigation included a review of:
understanding of the relationship between psychological and physiological processes during stressful and anxious states
Google scholar identifies over 3 million articles concurrently including stress and anxiety, indicating some level of association or correlation.
Stress and anxiety appear to be associated in heart disease (Chauvet-Gelinier & Bonin, 2017).
Neuropeptides have been identified that concurrently relate to stress and anxiety (Heilig, 2004; Cohen, 2012).
The Diagnostic and Statistical Manual of Mental Disorders (DSM-5), lists the adjustment disorders (page 286) concurrently with stress and anxiety. Interestingly, the DSM lists the word 'stress' 237 times and 'anxiety' 1280 times.
The Oxford and Collins dictionary lists anxiety and stress as synonyms. Merriam Webster lists them as near synonyms.
One definition of synonym is that you can use two words interchangeably in a sentence without loss or alteration of meaning.
Anxiety and stress are both abstract nouns and emotions, being able to be used in the sentence: "I feel a sense of anxiety" and "I feel a sense of stress".
The curators of the Oxford and Merriam Webster dictionaries appear to believe that anxiety and stress are closely associated.
My own research is in the lexical analysis of personality, emotion and behaviour (Mobbs, 2020). The words stressed and anxious can be visualised as follows. It is visually apparent that the terms are highly related, possibly synonyms. The question mentions Big-5; both anxious and stressed are in the region of the atlas denoted by the Big-5's neuroticism dimension.
A range of therapies appear to be targeted at concurrently dealing with stress and anxiety, such as:
Group therapy (White, 1992)
Cognitive behavioral therapy (Hopkinson, 2019)
Dialectical behavior therapy (Fitzpatrick, 2019)
Music therapy (Umbrello, 2019)
Physical exercise (Mikkelsen, 2017)
Chauvet-Gelinier, J. C., & Bonin, B. (2017). Stress, anxiety and depression in heart disease patients: A major challenge for cardiac rehabilitation. Annals of physical and rehabilitation medicine, 60(1), 6-12.
Mikkelsen, K., Stojanovska, L., Polenakovic, M., Bosevski, M., & Apostolopoulos, V. (2017). Exercise and mental health. Maturitas, 106, 48-56.
White, J., Keenan, M., & Brooks, N. (1992). Stress control: a controlled comparative investigation of large group therapy for generalized anxiety disorder. Behavioural and Cognitive Psychotherapy, 20(2), 97-113.
Hopkinson, M. D., Reavell, J., Lane, D. A., & Mallikarjun, P. (2019). Cognitive behavioral therapy for depression, anxiety, and stress in caregivers of dementia patients: A systematic review and meta-analysis. The Gerontologist, 59(4), e343-e362.
Fitzpatrick, S., Bailey, K., & Rizvi, S. L. (2019). Changes in Emotions Over the Course of Dialectical Behavior Therapy and the Moderating Role of Depression, Anxiety, and Posttraumatic Stress Disorder. Behavior Therapy.
Umbrello, M., Sorrenti, T., Mistraletti, G., Formenti, P., Chiumello, D., & Terzoni, S. (2019). Music therapy reduces stress and anxiety in critically ill patients: a systematic review of randomized clinical trials. Minerva anestesiologica, 85(8), 886-898.
Heilig, M. (2004). The NPY system in stress, anxiety and depression. Neuropeptides, 38(4), 213-224.
Cohen, H., Liu, T., Kozlovsky, N., Kaplan, Z., Zohar, J., & Mathé, A. A. (2012). The neuropeptide Y (NPY)-ergic system is associated with behavioral resilience to stress exposure in an animal model of post-traumatic stress disorder. Neuropsychopharmacology, 37(2), 350-363.