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.

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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.)

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The Oxford English Dictionary lists the following definitions:

disease, n.

1 Absence of ease; uneasiness, discomfort; inconvenience, annoyance; disquiet, disturbance; trouble. (For long Obs. but revived in modern use with the spelling dis-ease.)

2 A condition of the body, or of some part or organ of the body, in which its functions are disturbed or deranged; a morbid physical condition; ‘a departure from the state of health, especially when caused by structural change’ (New Sydenham Soc. Lexicon). Also applied to a disordered condition in plants.

3 fig. A deranged, depraved, or morbid condition (of mind or disposition, of the affairs of a community, etc.); an evil affection or tendency.

disorder, n.

1-3 Absence or undoing of order or regular arrangement; confusion; confused state or condition. ... Disturbance, commotion, tumult; esp. a breach of public order, riot, mutiny, outrage.

†4 Disturbance or agitation of mind, discomposure. Obs.

5 A disturbance of the bodily (or mental) functions; an ailment, disease. (Usually a weaker term than disease n., and not implying structural change.)

As we can see, the common meanings of disease and disorder, in our context, tend towards:

Disease

• a physiological dysfunction caused by structural change

Disorder

• a physiological dysfunction not caused by structural change, or
• a psychological dysfunction (caused by a physiological dysfunction, learning or the environment)

The use of the words disease and disorder by medical experts will likely be influenced by this lay meaning of the two words. Here are some definitions given by medical dictionaries:

Dorian, A. F. (1987). Elsevier's Encyclopaedic Dictionary of Medicine

• disease Any impairment of the normal state of the organism, interrupting or affecting the performance of its vital functions. More specifically, all physical and mental reactions to some noxious agent, an injury, a defect, a deficiency, or a degenerative process.
• disorder A condition characterized by a derangement of normal functions of the body.

Stedman, T. L. (1995). Stedman's Medical Dictionary (26th ed.)

• disease 1. An interruption, cessation, or disorder of body functions, system, or organs. SYN illness, morbus, sickness. 2. A morbid entity characterized usually by at least two of these criteria: recognized etiologic agent(s), identifiable group of signs and symptoms, or consistent anatomical alterations. SEE ALSO syndrome. 3. Literally, dis-ease, the opposite of ease, when something is wrong with a bodily function.
• disorder A disturbance of function, structure, or both, resulting from a genetic or embryologic failure in development or from exogenous factor such as poison, trauma, or disease.

Becker, E. L., et al. (eds). (1986). International Dictionary of Medicine and Biology

• disease A condition which alters or interferes with the normal state of an organism and is usually characterised by the abnormal functioning of one or more of the host's systems, parts, or organs. It may be due to an unknown cause or may result from an inherent metabolic or structural deficiency, including congenital and hereditary defects and degenerative processes, or from such factors as stress, noxious stimuli, toxic agents, injury, or infection. A given disease is often manifested by a characteristic set of signs and symptoms, although a host organism can be asymptomatic while having microscopic, serologic, or immuniologic evidence of diseease. • Disease is usually distinguished from injury, the disruption of an organism's integrity, espeially by an external agent, and often from syndrome, a complex of symptoms descriptive of a disorder, especially a particular combination of phenotypic manifestations.
• disorder An alteration of the function or struture of an organ or the body as a whole.

Dorland, W. A. N. (1994). Dorland's Illustrated Medical Dictionary (28th ed.)

• disease any deviation from or interruption of the normal structure or function of any part, organ, or system (or combination thereof) of he body that is manifested by a characteristic set of symptoms and signs and whose etiology, pathology, and prognosis may be known or unknown.
• disorder a derangement or abnormality of function; a morbid physical or mental state.

As you can see, medical experts love clear, distinct, and unambiguous, definitions.

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