The traditional way in which the field of psychiatry classifies mental disorders is as "organic versus non-organic". However, as of 1992 there has been a lot of debate arguing the removal of the term "organic" as anachronous and of a need to be broken into additional subgroups of conditions that happen phenomenologically.
"Organic" is something that happens naturally within the human brain as a result of physical and bodily processes. The most commonly known organic mental disorders as they are classified by the DSM-IV (the V is already out) are cognitively-based:
Within those categories we can find:
- mental retardation
- generalized anxiety disorder
- bipolar disorder
Notice how these three basic organic disorders do not seem to comprise every single manifestation of cognitive mental disorders as they seem to continuously pop up in today's society. This is why the argument arises about changing the name "organic" to something more comprehensive.
Non-organic mental disorders are those caused by external factors such as drug addiction, some forms of alcoholism (let's not include the theoretical foundations of inherited alcoholism), environmental changes (seasonal depression), allergies, and other additional factors.
Something "inorganic" is something made neither from plant nor animal, or being altogether inanimate. That is a misnomer for non-organic.