Organic chemistry  is "the study of carbon-containing compounds (typically chains of carbon atoms) and their properties". (S.S. Zumdahl, Chemistry)
Organic compounds  are carbon-containing compounds made of chains or rings like nutrients or plastics.
Organic chemistry was the study  carbon-containing compounds made by organisms until Friedrich Wöhler synthesized the substance from urine called urea CH₄ON₂).
Today this part of organic chemistry is called Biochemistry.