The subject area of Chemistry is a very broad area. So, it is classified into sub-branches like inorganic chemistry, organic chemistry, physical chemistry, quantitative chemistry and many more. But when the basis is on the composition of elements, it is divided into inorganic and organic chemistry. Compounds containing the element Carbon are all under organic chemistry. If they do not contain carbon, they are considered as inorganic.
During the early times, the only differentiation between these two sub branches is the vital theory. This theory proposes that all things that have life can be only made by nature alone are inorganic. But thing was disproved by Wohler when he was able to synthesize urea from inorganic compounds. Thus, today the only differentiation is the carbon atom.
