Psychologists are AHPRA (Australian Health Practitioner Regulation Agency) registered professionals who are required to undertake university level training that meets certain training requirements and ethical standards. They are specifically trained in human behaviour and mental health. Some psychologists undertake additional training in specific areas of practice (such as clinical psychology, occupational psychology, or education and developmental psychology). The study of clinical psychology involves the assessment, diagnosis and treatment of mental illness from a scientific framework.
A Psychiatrist is first and foremost a medical doctor who specialises in the assessment, diagnosis and treatment of mental disorders. They undergo extensive training in their chosen field. Psychiatrists can prescribe medication and tend to treat the more complex and serious mental illnesses.
Counsellors can provide support in lots of areas in life. They can come from all sorts of training backgrounds and offer a range support. Technically anyone can call themselves a counsellor in Australia as there is no regulation of the industry. However, many counsellors volunteer to register with national counselling organisations in Australia such as PACFA (Psychotherapy and Counselling Federation of Australia). These organisations require members to meet minimum requirements for training, experience and competence and to adhere to a range of ethical standards.
There are many other professionals who also work in the mental health space including Occupational Therapists and Mental Health Social Workers who can offer a range of support.
What is most important is to find someone who best fits your needs for the issues you are dealing with and who is able to guide you towards the best possible outcomes for you.