I read GP's last paragraph as distinguishing between the use of "disabled people" vs. "people with disabilities," rather than between the use of "disabled" (or words with the same root) vs. other words.

My company did some work for an organization that supported people with disabilities in the workforce. The client stressed the importance of the distinction between using "people with disabilities" as opposed to "disabled people," with the former being much preferred because - due to its structure - it puts the focus (i.e. the first word) on "people" rather than "disabled/disability".