If you use your degree as a Ph.D. in clinical social work to gain employment that is really in the realm of clinical psychology, you will be looked at, and rightly so, as someone who took a backdoor route to a career in clinical psychology.
If you want to be a clinical psychologist, get a degree in clinical psychology. If you want to be a clinical social worker, be it at the Master's level or Ph.D. level, then you should get a degree in clinical social work.
They are different degrees for a reason.
See below, the overlap is actually pretty narrow in that Clinical Social Workers use therapy as a tool to achieve Social Work outcomes, and not the treatment of mental illness or to provide assessment of mental abilities. On the other hand, the primary purpose of clinical psychology is NOT social change, social justice, community organizing, or social policy change. It is important to acknowledge that there is overlap, but mostly in that public health policy becomes an area of interest to both disciplines.
The International Federation of Social Workers defines Social Work as: "The social work profession promotes social change, problem solving in human relationships and the empowerment and liberation of people to enhance well-being. Utilising theories of human behaviour and social systems, social work intervenes at the points where people interact with their environments. Principles of human rights and social justice are fundamental to social work."
Practice:
"Social work addresses the barriers, inequities and injustices that exist in society. It responds to crises and emergencies as well as to everyday personal and social problems. Social work utilizes a variety of skills, techniques, and activities consistent with its holistic focus on persons and their environments. Social work interventions range from primarily person-focused psychosocial processes to involvement in social policy, planning and development. These include counseling, clinical social work, group work, social pedagogical work, and family treatment and therapy as well as efforts to help people obtain services and resources in the community. Interventions also include agency administration, community organization and engaging in social and political action to impact social policy and economic development. The holistic focus of social work is universal, but the priorities of social work practice will vary from country to country and from time to time depending on cultural, historical, and socio-economic conditions."
On the other hand Clinical Psychologists (according to division 12)
"The field of Clinical Psychology integrates science, theory, and practice to understand, predict, and alleviate maladjustment, disability, and discomfort as well as to promote human adaptation, adjustment, and personal development. Clinical Psychology focuses on the intellectual, emotional, biological, psychological, social, and behavioral aspects of human functioning across the life span, in varying cultures, and at all socioeconomic levels."
Practice:
"The Clinical Psychologist is educated and trained to generate and integrate scientific and professional knowledge and skills so as to further psychological science, the professional practice of psychology, and human welfare. Clinical Psychologists are involved in research, teaching and supervision, program development and evaluation, consultation, public policy, professional practice, and other activities that promote psychological health in individuals, families, groups, and organizations. Their work can range from prevention and early intervention of minor problems of adjustment to dealing with the adjustment and maladjustment of individuals whose disturbance requires then to be institutionalized.
Practitioners of Clinical Psychology work directly with individuals at all developmental levels (infants to older adults), as well as groups (families, patients of similar psychopathology, and organizations), using a wide range of assessment and intervention methods to promote mental health and to alleviate discomfort and maladjustment.
Researchers study the theory and practice of Clinical Psychology, and through their publications, document the empirical base of Clinical Psychology. Consultants, Teachers, and Clinical Supervisors share the Clinical Psychology knowledge base with students, other professionals, and non-professionals. Clinical Psychologists also engage in program development, evaluate Clinical Psychology service delivery systems, and analyze, develop, and implement public policy on all areas relevant to the field of Clinical Psychology. Many Clinical Psychologists combine these activities.
Assessment in Clinical Psychology involves determining the nature, causes, and potential effects of personal distress; of personal, social, and work dysfunctions; and the psychological factors associated with physical, behavioral, emotional, nervous, and mental disorders. Examples of assessment procedures are interviews, behavioral assessments, and the administration and interpretation of tests of intellectual abilities, aptitudes, personal characteristics, and other aspects of human experience and behavior relative to disturbance.
Interventions in Clinical Psychology are directed at preventing, treating, and correcting emotional conflicts, personality disturbances, psychopathology, and the skill deficits underlying human distress or dysfunction. Examples of intervention techniques include psychotherapy, psychoanalysis, behavior therapy, marital and family therapy, group therapy, biofeedback, cognitive retraining and rehabilitation, social learning approaches, and environmental consultation and design. The goal of intervention is to promote satisfaction, adaptation, social order, and health."