The phrases "the mentally ill" and "people with mental illness" sound very similar, but found we have very different reactions when we hear them. In the study, people who read passages with the term "the mentally ill" were more likely to believe that individuals with such a diagnosis should be controlled and isolated than those who read the same scenarios with the term "people with mental illness." The results were the same when researchers tested college students, older adults, and even counselors (yes, the ones who regularly treat people for mental health issues!).
Making the small linguistic change—from what a person is to what a person struggles with—can impact our reactions and how people with mental illness feel. After all, if you broke your leg you wouldn't want to be called a broken-leg person, right?