Biochemisty is the study of chemical processes in biological systems.
Organic chemisty is the study of compounds containing carbon-carbon or carbon hydrogen bonds.
There is an important overlap (organic biochemistry) to be sure, but each dicipline includes topics excluded from the other.
There is inorganic biochemisty in which inorganic compounds important to life are studied. And Organic chemistry contains many areas in which chemicals not found in biological systems are studied, or in which important biochemicals are studies outside biological systems. Much works in Organic synthesis involves either chemical not found in natural biological systems or used diffently.