What is your preferred terminology for people whose brains work differently?

@MyNewtBoobs quarreled with me when I was complaining about terms like crazy, insane, nuts, and the like. I said I preferred the term “mental illness.” She replied as follows”

Mental illness is, at best, incorrect most of the time. For bipolar, it’s a disorder, not a disease or illness (the organic, genetic part – it’s a bit different with syphilis). But mostly, illness seems to say that you’re sick, which you aren’t. Most mental disorders you simply think and feel differently than the “normal” population does, but you aren’t sick, you aren’t wrong, you aren’t twisted. Mental illness suggests that you should spend all your time popping pills and trying to get better and be normal; mental disorder says “It’s different, I work with it, now GTF over it.” Disorder aims to create a wider circle of tolerance, whereas illness does the exact opposite – it stigmatizes and excludes. Course, if you have a mental disorder or illness or whatever you want to call it, you can call it whatever the fuck you want to. And I’m not hugely offended by it most times, unless people have given me a reason to think that they aren’t just saying a word and my issues with “illness” are their opinion at large.

I think this is a well-thought-out point of view. So it made me wonder what others think about the terminology that is used for people with manic-depression (bipolar) or schizophrenia or depression or any of the other conditions like these.

Is calling someone crazy offensive? How about saying “mental disorder,” or “mental illness?” What do these terms—both medical and colloquial—mean to you? Which ones are dismissive and which ones a respectful?