It sounds like you are using "theory" and "law" for things like "rules" as physicists sometimes do.
Traditionally mathematicians will call any significant result worth remembering a theorem. The Pythagorean Theorem is a archetypical example.
We use "law" sometimes too, but it's really the exception to the rule. (Like "Law of quadratic reciprocity.") There really isn't a standardized use of "law" in mathematics.
In mathematics, a theory is a large coherent group of results in the same field of study. It's used in the literal sense as "body of knowledge," not like "rule." So you can talk about "the theory of groups."
At any rate,
since there is no formal definition of "law" or "theory" in mathematics, this is not so much a question about math as it is about language. You might try on english.SE.
English dictionary, I choose you!
Theory : 3.Mathematics . a body of principles, theorems, or the like, belonging to one subject: number theory.
Theorem: 1.Mathematics . a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas.