Dementia is a general term that refers to a loss of cognitive abilities (memory and thinking) due to a brain disorder.
The diagnosis of a dementia, by itself, does not imply that the person has an irreversible or even a progressive disorder. Some disorders that cause dementia are stable (i.e., the person doesn't get worse over time), and some are reversible (i.e., the person improves over time, especially with treatment).
Alzheimer's disease is a specific neurological disease. It is the most common cause of dementia in the elderly. While we don't yet have a cure for Alzheimer's disease, and it is currently irreversible, there are several treatments that can lessen the symptoms in some patients. For this reason, early detection is important.