Is there a way for the Dr. to know for sure if my mother has dementia or Alzheimer's?

Are you asking if she has either one or the other? Alzheimer’s is a form of dementia. Back in the day, this disease and all it’s forms were called “senility” or “hardening of the arteries”. As Mac says, they are both treated the same way. There is no cure. Saavy people realize what’s happening and get Power of Attorney before their Loved One is legally deemed incompetent because after that, a POA is worthless.

If you suspect something is amiss, there are tests and evaluations that can be done. You can consult with a neurologist. Use this site to do research on symptoms and treatments.