The terms "organic arsenic" and "inorganic arsenic" are not trying to describe two different kinds of the element arsenic. They are describing the other elements to which the arsenic atoms are bound. Arsenic is a highly reactive element and as a result you don't find it in a pure form in nature.
Organic arsenic is arsenic bound to hydrogen and carbon. This is the kind that passes harmlessly through the human body. The stable carbon and hydrogen bonds keep the arsenic atoms securely locked into molecules that will not react with the rest of the body.
Inorganic arsenic is generally bound to atoms that are more volatile, such as chlorine, sulfur and oxygen. These molecules tend to break apart in the human body, allowing the arsenic to actually react.
The test Oz did failed to differentiate between these two kinds of arsenic containing molecule, making the results meaningless for evaluating the safety of the juice.