Often, it is very difficult to tell if someone is having memory loss from multiple small strokes, or from Alzheimer's disease. A particular challenging part of the problem is that
Alzheimer's can only be definitively diagnosed by looking at the brain under a microscope - in other words, in a post-mortem examination.
However, some ideas to ask your doctors about would be 1) getting an MRI of the brain, 2) getting a PET scan of the brain, and 3) getting a Neuropsychological evaluation. Each of these tests can help pin down the diagnosis.
An MRI will often show in great detail the amount of stroke burden the patient has, which looks quite different from the frequently atrophied appearance of a brain of an Alzheimer's patient. PET scanning will help show metabolic disturbances typical for Alzheimer's disease, which should be different from those of someone with multiple strokes. Finally, a good NeuroPsychologist will do comprehensive testing of all areas of cognition, and can usually pin down specific areas of brain functioning that are effected by these two diseases - often leading to a specific diagnosis.