If I may add - toxicological chemistry is the investigation or understanding of the ADVERSE effects elicited by a chemical on cellular/tissue constituents. Both biochemistry and toxicological chem involve assays that can be described or cross both disciplines of chem and biochem. Both biochemistry and toxicology chem study molecular as well as cellular aspects, however I would say that what distinguishes toxicological chem is that one is specifically looking at the adverse/negative effects on the human/animal model brought about by a specific chemical of interest.
Biochemistry is a laboratory based science that brings together biology and chemistry ( study the chemical basis of biology) . By using chemical knowledge and techniques, biochemists can understand and solve biological problems
Toxicological chemistry involves the study of the adverse effects of chemical substances on living organisms, the detoxification mechanisms, and the practice of diagnosing and treating exposures to toxins and toxicants.
In a very simple way, I define biochemistry as the scientific study of the chemical reactions that start, maintain/affect life.
Toxicological chemistry is different from general biochemistry because of the focus; toxicological chem. relies on a Working knowledge of biochemistry.
I agree with the answers provided above. A toxin is foreign within the biological space which biochemistry defines as life. The focus of Tox. Chem. is the adverse effect of toxins