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They're actually the same thing, exactly.

"A mental disorder, also called a mental illness[2] or psychiatric disorder, is a behavioral or mental pattern that causes significant distress or impairment of personal functioning."

https://en.wikipedia.org/wiki/Mental_disorder

Illness is common parlance, whilst disorder is the professional term.

It's also formally acknowledged in the DSM, so it's definitely not debated... unless you're talking about antivaxers types that think moonbeams cure stuff.

I'll shut up now.