The key difference between rate expression and rate law is that rate expression gives the rate of appearance or disappearance of products or reactants, whereas rate law gives the relationship between rate and concentration or pressure of reactants.
When one or more reactants are converted to products, they may go through different modifications and energy changes. The chemical bonds in the reactants break, and new bonds are formed to generate products that are totally different from the reactants. This chemical modification is known as chemical reactions. Rate expression and rate law are important chemical concepts we can describe in chemical reactions.