Dementia is a symptom, and Alzheimer's disease is the cause of the symptom.
Alzheimer's Reading Room
Dementia is the gradual deterioration of mental functioning, such as concentration, memory, and judgment, which affects a person’s ability to perform normal daily activities.
Go here to read more about Dementia.
In a nutshell, dementia is a symptom, and Alzheimer's disease is the cause of the symptom. When someone is told they have dementia, it means that they have significant memory problems as well as other cognitive difficulties, and that these problems are severe enough to get in the way of daily living.
Go here to read more about the Difference between Alzheimer's disease and dementia.