It is possible that a disability is the cause of a handicap. For example, if a person a disability that prevents a person from being able to move their legs would result in a handicap in driving. Disabled people do not have to be handicapped, especially if they can find a way around their disability. For example, Braille for the visually impaired or wheel chairs for those who cannot walk.
A disability is an inability to execute some class of movements, or pick up sensory information of some sort, or perform some cognitive function, that typical unimpaired humans are able to execute or pick up or perform. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these.
A handicap is an inability to accomplish something one might want to do, that most others around one are able to accomplish.
edit What is politically correct to say?
It is politically correct to say that a person has a disability and it's impolite to call someone handicapped.
"Disability vs Handicap." Diffen.com. Diffen LLC, n.d. Web. 29 Jul 2014. < http://www.diffen.com/difference/Disability_vs_Handicap >