What you said is often true but not always. Some communities prefer person-first language, some prefer identity first language.

For example, generally speaking, “autistic people” is preferred over “people with autism”. The reasoning being “this is just part of who I am, it’s not an affliction that I have.”

I’m not autistic but I have lots of friends who are, and they all prefer to say “I’m autistic” rather than “I have autism”.