Difference between Rate Law and the law of mass action?

Rate Law: In rate law, the concentrations of reactants are raised to some power which may or may not be equal to the Stoichiometric coefficient of the reaction.

Law of Mass Action: In the law of mass action, the concentrations of reactants and products are raised to the power of their Stoichiometric coefficient.

The main difference between rate law and law of mass action is that, rate law is given considering only the reactants of a reaction whereas law of mass action is given considering both reactants and products of a reaction.

The Rate Law cannot be determined by just looking at the given chemical equation but, instead, can be determined only experimentally. However, the Law of Mass Action can be determined by just looking at the chemical equation.

According to this “Law of Mass Action”, for a given reaction of the form:
aA + bB —→ Products,
the rate of reaction = k[A]^a[B]^b
where k is the equilibrium constant.

But experimentally, it has been found out that the rate of reaction may not necessarily depend on all the ‘a’ concentration terms of A or on all the ‘b’ concentration terms of B but only on some partial amount of the total concentration of A or B, say, x and y respectively.
i.e.,
Rate of Reaction = k[A]^x[B]^y
where, x and y may or may not be equal to a and b.
This above expression is called Rate Law.