Psychiatry & Psychology--General/mental health
What is the difference between mental illness and mental disorder?
I see it used interchangeably but when placing a patient in a mental health facility, you have to distinguish if they are either one of the two.
Interesting question -- for which I wish I had a definitive answer.
In North America, mental illness/disorder/disease are used interchangeably, as you say. (We could add mental handicap, though that may imply retardation.) The most generally accepted term these days is disorders, as that is used in the International Classification of Diseases [ironically] as well as the current DSM.
Although they mean the same, with facilities there may be legal issues because of their powers, usually to confine and to treat. A similar issue is that of statistics reporting, which would have its own specific language. And another may be insurance. For each of these contexts, there may well be specific definitions.
Being on the other side of the world, I do not know what these defining issues are in your country. For instance, it may be that in Australia somebody can be forcibly confined and treated for a mental illness but not for a mental disorder. And there may be some circularity, for instance, a "mental illness" is one that is expected to respond to appropriate treatment, whereas a "mental disorder" could be something like paranoia or disagreeableness.
I should add that what a psychological problem is called can vary according to the profession doing the diagnosis, the relevant laws and policies, the time and place, and the orientation of the diagnostician. The most power is in the hands of psychiatrists, and as medical doctors they may prefer "illness" for obvious reasons.
I'm sorry that in all that I've said I have not given a direct answer to your question, but that's the best I can do from here. Thanks for asking us, and if you think there's something I might be able to add, feel free to send a follow-up.