Biochemistry is the study of molecules (enzymes, proteins, lipids, carbohydrates, etc.) and their chemical reactions which occur in living organisms. This field often focuses on questions regarding structures, interactions between molecules, and the mechanisms of chemical reactions. For instance a biochemist would be very interested in the amino acid residues in an enzyme's active site and how they contribute to it's function, or what regions of protein XYZ are capable of binding DNA.
Biochemical analysis evaluates gene expression by sampling enzymes and specific substances that are produced by the body. This analysis indicates the level of functionality of a gene.
Compare this to genetic studies, which researches the gene sequence, biological pathway and how it functions in an organism. Genetic studies are used to track the occurence and patterns of inherited diseases such as Huntingtons Disease or non-inherited diseases, such as Autism. A lot of genetic studies are done using model organisms like bacteria in order to be able to simply evaluate gene expression.