Deaf with a lowercase “D” is the medical term for people who have lost their hearing. People who identify as deaf have a spoken language as their first language. They may or may not know sign language. People who are deaf may have an assistive device such as a hearing aid or cochlear implant.
Typically, people who identify as deaf do not know sign language or participate in Deaf culture.
Deaf with an uppercase “D” is a cultural term for people in the Deaf community. Deaf people use sign language as their primary language and share a common culture.
For information about American Deaf Culture, read here. https://www3.gallaudet.edu/clerc-center/info-to-go/deaf-culture/american-deaf-culture.html