To call somebody "a disabled person" — an autistic person, for example — is to use "identity-first" language. It puts the disability first in the phrase. To say that they are, instead, a "person with a disability" — e.g., a person with autism — puts their personhood first, and their disability as just one element that makes up their whole personhood. You're more likely to have heard of (or used) person-first language: According to the National Center on Disability and Journalism, it stems from a shift to rename the "Education for All Handicapped Children Act" in 1990, to "Individuals With Disabilities Education Act." Person-first language is considered more PC in North America, and some people still find this terminology preferable. These terms of reference are used in disabled communities all the time, and they reflect bigger ideas about what disability is, how it affects or interacts with your personhood, and how other people see you.
The difference between the perspectives essentially boils down to personhood and disability: is it something that you have, or something that's at the core of your identity? Among autistic people, identity-first language is popular, because they often feel it's such a strong part of who they are, not something that's happened to them. Lydia Brown of the Autistic Self-Advocacy Network, who is autistic, explains in an essay that while she has previously encountered arguments that because we say "person with cancer" rather than "cancerous person," we should do the same for autism, but she argues strenuously against that point:
"Cancer is a disease that ultimately kills if not treated or put into long-term remission. There is absolutely nothing positive, edifying, or meaningful about cancer. Cancer is not a part of a person’s identity or the way in which an individual experiences and understands the world around him or her. It is not all-pervasive. Autism, however, is not a disease. It is a neurological, developmental condition; it is considered a disorder, and it is disabling in many and varied ways. It is lifelong. It does not harm or kill of its own accord. It is an edifying and meaningful component of a person’s identity, and it defines the ways in which an individual experiences and understands the world around him or her. It is all-pervasive."
But that's not the way all people think of it. The American Psychological Association recommends that professionals use person-first language ("person with disability") in their everyday discourse, because the adoption of person-first language was a conscious movement away from the previous (and seriously offensive) ways of referring to disabled people. It was meant to consciously reaffirm the humanity and personhood of the disabled person, rather than make their disability their defining feature without their consent. The International Federation of Adapted Physical Ability takes a person-first perspective, explaining:
"In person-first language, an intellectual disability is viewed as one aspect of a person. This person may have many other attributes such as being tall or short, being blond or brunette, loves baseball or loves football, loves watching TV or loves reading books, loves pizza or loves hamburgers, etc. Having an intellectual disability is just one of many characteristics that defines a person."
What people think about the issue, interestingly enough, appears to depend on where they stand within the disabled community itself. A research paper published in 2015, which surveyed people in the autistic community in England, looked at how different people viewed different types of language, and found an intriguing divide. While autistic people themselves often expressed a preference for identity-first language, their families often wanted person-first language and rejected identity-first language and terms like "Aspie", for Asperger's. In her essay, Lydia Brown mentions a meeting in which a mother describes "cringing" at the word "autistic" because it had such negative connotations in her childhood, and actively advocating for person-first language.