In normal usage, a handicap is a drawback you can easily remedy, but a disability is much worse: you’re just unable to do something. But many people with disabilities and those who work with them strongly prefer “disability” to “handicap,” which they consider an insulting term. Their argument is that a disability can be compensated for by—for instance—a wheelchair, so that the disabled person is not handicapped. Only the person truly unable by any means to accomplish tasks because of a disability is handicapped.
The fact that this goes directly counter to ordinary English usage may help to explain why the general public has been slow to adopt it, but if you want to avoid offending anyone, you’re safer using “disability” than “handicap.”
Many of the people involved also resent being called “disabled people”; they prefer “people with disabilities.”
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