I don’t see that this distinction even needs to be made. Whichever word you choose, the focus should be on the fact that a person’s {mental, physical} health is

I don’t see that this distinction even needs to be made. Whichever word you choose, the focus should be on the fact that a person’s {mental, physical} health is suboptimal in some way. And the question then is: what sort of intervention will help — psychological or physiological?