What is the difference between being hard of hearing and being deaf? The answer is not simple, and is getting even harder to define with the growth of cochlear implants.
Medically, the definition depends on how many decibels of hearing loss you have. A loss that is less than profound is generally considered hard of hearing. The article Types, Degrees of Hearing Loss gives an overview of what hearing loss level would be considered deaf or hard of hearing.
When I was growing up, there was an expression, "he's deaf but with hearing aids, he functions like hard of hearing." I've always been deaf, but when I wore hearing aids people often considered me hard of hearing because of how well I functioned with the hearing aids. Even other deaf students thought I was hard of hearing when my audiogram said I was deaf.
Then there is the cultural definition. According to the cultural definition, being deaf or hard of hearing has nothing to do with how much you can hear! It has to do with how you identify yourself - do you identify more closely with hearing people or with deaf people? Many medically hard of hearing people consider themselves culturally deaf.
This one is my own invention. Have you ever heard a person who was medically and functionally deaf insist, "I'm not deaf, I'm hard of hearing?" This statement is often made by people with hearing loss who are ashamed of how deaf they are.
Are people with cochlear implants whose hearing losses are reduced to as little as 20 db hard of hearing or deaf? In my opinion, the answer is, "both." I say both because when a cochlear implantee has the implant on and can hear that well, they are hard of hearing. When the implant is off and they can not hear anything, they are deaf. The same is true for hearing aids. Long ago, I would say that I was "on the air" when wearing my hearing aids and functioning like a hard of hearing person, but "off the air" when not wearing the hearing aids and unable to hear anything.
The National Association of the Deaf addressed this same question in their FAQ page, Difference Between Deaf and Hard of Hearing.