A biochemist is a person whose work is the chemistry of living things. In a university they might watch how a protein folds. In a hospital lab they might run blood tests. In a company they might help design a medicine or check what is in a food. It is a trained, fairly formal job-word: you would not call a high-school student a biochemist just because they like the class. Though actually, real job titles are messy. The same person might be called a chemist, a molecular biologist, or a lab scientist depending on the building they work in. Biochemist is the clear word when the work is specifically life-chemistry, not chemistry in general and not biology with the chemistry left out.