My short answer is that I think they are labels for the medical profession's excuses for not finding out the real, physical problem that's happening within afflicted individuals and fixing it/them. Meaning, the mind is part of the body, so if there's something wrong with it we should treat it just like we treat any other medical issue/disease/illness.
Particularly insulting and stigmatic, in my opinion, is when psychiatric issues are referred to as "behavioral health" issues. After all, it wasn't long ago that infertility, erectile dysfunction, heart problems, seizures, migraines, Alzheimer's, allergies, and MANY other common diseases treated physically today were considered "psychiatric" or "mental health" issues. Even being gay/lesbian was considered a psychiatric illness until just a few years ago--seriously and literally!
Hmm. Do you think our society has something to learn yet about "psychiatric" disorders? The brain changes in "psychiatric" patients can be measured on EEGs, PET scans, MRIs, sleep tests, and even autopsies... And they respond well in general to medicines, just like "physical" illnesses... "If it acts like a duck and quacks like a duck..." as the phrase goes....
Maybe that was my long answer or rant after all. LOL