Problem in the first case: Alzheimer's.
Problem in the second case: Broken bone.
Alzheimer's is what we call a specific problem in the brain and it has specific symptoms. This is a type of dementia, but it is distinct from other types of dementia like Parkinson's, ALS, etc. What's gone wrong in the brain has some behavioral similarities, but it is distinct upon examination of both behavior and the patient's brain itself.
Just like say, a compound fracture of the radius is a specific problem in the arm with specific symptoms. It is a type of damage to the bone, but distinct from a simple fracture, osteoporosis, etc.
Brains don't have problems. We have problems.