Difference between brain disease and brain disorder Is there any difference between the terms brain disease and brain disorder? They are often used in combination without specifying the difference, e.g. here.
There are many who will tell you authoritatively that a disease is acquired (e.g. infection, cancer, etc.) whereas disorder is something curable or genetic. These are imprecise and untrue. Basically a disturbance in normal functioning can be either a disorder or a disease, regardless of it's curability or method of acquisition. 

From your link, the second entry (for acid lipase disease) contains this information:


  Two rare lipid storage diseases are caused by the deficiency of the enzyme lysosomal acid lipase: Wolman’s disease... is an autosomal recessive disorder... Infants with the disorder appear normal at birth... Cholesteryl ester storage disease (CESD) is an extremely rare disorder...


and


  Alexander disease is one of a group of neurological conditions known as the leukodystrophies, disorders that are the result of abnormalities in myelin... Alexander disease is a progressive and often fatal disease.


This might lead you to deduce that the disease is the manifestation, whereas disorder is the source. Though I would say that this is as close to a real distinction you'll find, even that doesn't consistently hold up. We talk about infectious diseases though we know the etiology and pathology, and inherited diseases and disorders. Mental diseases are mostly disorders regardless of their genetics.

The truth is that nomenclature is subjective. It has something to do with history (if the person who discovers or elucidates the disorder an illness names it a disease, a disease it will tend to remain, e.g. Huntington's disease/Crohn's disease), precedent, and advances in understanding. I think there is a tendency to name things disorders today, as disease carries certain connotations. It is all very subjective.

Edited to add: no disease or disorder occurs without some change in underlying structure. Creutzfeldt-Jakob disease (closely related to Bovine Spongiform Encephalopathy - also known as Mad Cow Disease) occurs in an inherited form, a sporadic form, and a transmitted form. In all cases, the etiologic agent is thought to be a self-replicating tiny bit of protein called a prion. Prions occur normally, and are replicated and broken down. When the abnormal prion (same chemical structure but a different spatial structure) is introduced, this new prion, because of it's different shape, cannot be broken down, accumulating in the brain, eventually to the extent that normal brain cells are destroyed by the stores of prion within the brain. The same can be said of any illness: something of normal order is disturbed (e.g. smokers and Chronic Obstructive Pulmonary Disease.)