Biomedical science is a multidisciplinary science that focuses on how cells, organs and systems function within the human body. It also looks at the functioning of the body during disease. It is basically the science underpinning human health. It includes topics such as anatomy, genetics, cell biology, biochemistry and molecular biology.
Biochemistry, on the other hand, is the chemistry behind various biological and metabolic processes. Some consider it a subset of biomedical science. It includes topics like enzymes, protein structure and folding.