I had an accident on vacation once and was hospitalized. As a result, for a short period of time, whenever I would get drunk I would experience 'word salad' - some words I was trying to say would get changed into some other word when they came out of my mouth. But I had no idea it was happening - I heard myself saying one word, but my mouth emanated a completely different word. I only became aware of it when someone told me about it when I was sober. All my other faculties were totally fine, it was just the words got mixed up.

It hasn't reoccurred, but i'm now very aware that what I experience as reality is completely subjective to how my brain is functioning. Anything I experience right now could be a different version of reality. But at the same time, now that i'm aware it has happened, I can keep that in mind and consider it in the future. I have to believe that different forms of mental illness allow for the same kind of self-awareness, but it depends entirely on what parts of their brain are functioning (like if they can control their emotions and think clearly, which is hard enough for "sane" individuals already)

The clinical term for this is "anosognosia", which describes a specific physical, neurological inability to be aware of their illness. They literally have damage in their brain which prevents self-awareness. Something like 50% of cases of schizophrenia have some degree of anosognosia as well.

This is a big part of why schizophrenia is so hard to treat. With other disorders like OCD, patients generally do know they are unwell and are willing to accept treatment to improve it. With schizophrenia, patients are often rigidly convinced they are already healthy and refuse to be treated. They are incapable of understanding that they have an illness.

It differs from person to person. I've met people who know that they suffer from schizophrenia, some who are unaware, but know hearing voices is abnormal, and some who has no idea.

There's a big difference between the three. The first, the ones who know and care about it - you probably won't even notice he/she is suffering from it, unless they tell you. The others.. yeah.

Source: used to be a med student and a trained hospital sitter.