In US English, the terms don't seem to be interchangeable. I suggest that the Asker investigate a little further to find out if the same applies to Australian English.
From UCLA:
"Although both clinical and health psychologists often examine mental health, the field of
clinical psychology primarily focuses on diagnosing, understanding, and treating mental disorders, whereas
health psychology examines the bidirectional relationship between mental and physical health" (emphasis added).
https://health.psych.ucla.edu/phd-in-clinical-psychology-ver...For a definition of
hospital psychology, check out my reference.