Although the lines between mental illness and demonization were sometimes blurred in the ancient world (often pejoratively; e.g. John 7:20; 10:20), the biblical authors certainly distinguished between natural and spiritual affliction. For instance, in Matthew 17:15 we see a boy who has seizures because he is demonized; yet in Matthew 4:24 we see that those who are demonized are distinguished from those who merely have seizures. Exhibiting symptoms associated with demonization carried no presumption that you were, in fact, demonized, because ancient peoples knew that those symptoms could occur naturally also.
It seems there is a particular Western chronological snobbery that assumes all ancient people were superstitious, inclined to attribute the slightest natural phenomenon to spiritual interference; while all Western people are scientifically detached, knowing better. But in fact, the situation today is very much like the situation then, because the psychology of people has not fundamentally changed in a few thousand years. Our knowledge of the natural world may have advanced (and our knowledge of the spirit world may have declined), but some people are still superstitious by nature, and some people still aren’t. If you doubt this, consider how many people you know who regularly check their horoscopes.
From what I have read, demonization can be mistaken for mental illness, but only for a while, or by those who are especially inimical to spiritual explanations. It is just fundamentally different to mental illness, in obvious ways. Speaking other languages and evincing paranormal abilities are simply not symptoms indicated in schizophrenia, psychosis or any other neurological illness.
Surprisingly (to me at least), secular psychologists are often more open to demonization as an explanation than you might expect, even if they don’t always agree with the Christian understanding of what that means. Here’s one good article where this is evidenced:
And here are a couple of other articles on the relationship between demonization and mental illness which I have found helpful; one from a pastor whose brother is a psychiatrist, and one from a secular psychiatrist who works with the Catholic Church:
Incidentally, the frequency and type of involvement the Catholic Church has in exorcism is itself an interesting topic. In my opinion, it illustrates how similar Roman Catholicism has become to Second Temple Judaism, where the Jews were largely unbelievers dressed up in pious traditions, and had worked out complex rituals for exorcism that were fairly ineffective. Compare this to the method modeled by Jesus, which amounts to, “Hey you—get out of there!”