In this uncapitalized form, the word "deaf" simply means unable to hear. It says nothing about the individual, the individual's language or culture. Some deaf people also consider themselves "Deaf" with a capital "D", which does imply a lot about their language and culture.
Technically, Deaf people, some hard of hearing people, and all late deafened people are deaf.
Some hard of hearing people, who might be completely unable to hear may still prefer to be called "hard of hearing" ... it's a personal choice.
Many Deaf people (note the capital "D") may prefer to be called Deaf instead of deaf, and are quite happy being Deaf and use sign language as a primary language ... again, it's a personal choice.
Many deaf people (note the lower case "d"), especially those who grew up with decent hearing, desperately wish that they were not deaf.
Some deaf people, who were "born deaf" have rejected Deaf Culture and done everything possible to survive in a "hearing world" using speechreading or other non-signing communication.