Heya Loghead.
This question comes up a lot and it confuses people sometimes.
Some opinions in here, like AlleyCat's, has got it right. It's all about personal preference, what's to stop Clark Kent from calling himself Superman or Victor Von Doom to call himself Dr. Doom.. or the Meji Samurais to nick themselves as Seii Taishoguns as "generals who destroy the East Barbarians".
It's all up to them or you for that matter.
To be politically correct..
If you use your hearing as a means to communicate, but have trouble understanding situations where the speaker has spoken either too fast, softly, or not clear enough for you to understand..
Then that's where Oral communication is your primary form of communicating, and what I would personally see label as "hard of hearing.. Hearing impaired/handicapped.. decreased hearing ability and/or perception."
When it comes to everyone who is deaf/hearing impaired-handicapped and we need to label ourselves to be politically specific to categorize each and every form of our deafness, then this is where we start saying stuff like:
Bilateral Deafness
Profound-Severe Deafness
Mild/Moderate Deafness
Sensorineural / Conductive Deafness..
etc..
We can be even more specific about our loss of hearing functions, there's a method of labeling deafness by the inference of capitalizing the D in the word Deaf.
Being
deaf (deaf culture, also known as little d as in the letter) would refer to associating yourself with the world that cannot hear well, which includes everyone.
Just like how you would distinguish between a Feral cat and a pet cat by saying "A wild
Feral Cat, and a Domestic
House Cat".
Being
Deaf (Deaf culture, the big D) would refer to a specific group of Deaf individuals within the deafs.
Deaf would refer to people who associate themselves as a "Pure breed" of the deaf people. Like, their lives is all done with Deaf methods, you don't associate with the hearing world for your everyday needs. They went to deaf school, they communicate in sign/written only, basically people who would avoid associating themselves with the hearing people. It's like in the cat example, we would call a particular cat not as a "Feral Cat, Domestic Cat", but more as like a "wild
Siamese feral cat, a Domestic
Calico House Cat". Its being specific to what kind of a deaf person they are.
I hope that makes sense.