I disagree with Kate about dropping the "people" and just saying "the disabled"
"people with disabilities" is an accepted PC term without being over the top
Have a look in the archives tho' - this has been discussed frequently.
With respect to your original question about the difference, the WHO definitions of "handicap" and "disbility" might help:
"Disability - "Any restriction or lack of ability to perform an activity in the manner or within the range considered normal for a human being." Here we are talking about things people cannot do.
Handicap - "A disadvantage for a given individual, resulting from an impairment or disability, that limits or prevents the fulfilment of a role (depending on age, sex and social and cultural factors) for that individual." This is in relation to a particular environment and relationships with other people.
Impairment: "Any loss or abnormality of psychological, physiological, or anatomical structure or function"
http://bmj.bmjjournals.com/advice/stylebook/d...HTH