A theory of x, is the ripened body of knowledge or more precisely a framework of concepts which has a correspondence with the facts within the field of knowledge-x and a logical relation among those concepts such that a consistent formal system giving a general view of dependency/inter-dependencies of its axioms can be formulated. The framework should be such that it is internally and externally consistent, simple (at level of axiom, theorems and whole theory) and, satisfies certain explanatory (explanatory adequacy: explaining a set of puzzles) and descriptive (descriptive adequacy: the elements that combine the puzzle and the explanation) demands.
We are free to chose any sufficiently well-defined equivalent formal system used to reconstruct the object-statements of a Theory. And the terms are internally and recursively defined, with the goal to have a referent.
Puzzles can only be made sense of in presence of a Programme/Theory/Paradigm. The paradigm and programme put constrains on the nature of descriptive and explanatory elements of a Theory.
Note: Descriptive and Explanatory adequacy are not the same as observational adequacy, which would mean something like accounting for “all of the relevant phenomenon”. The goal of a theory is to chip away the non-essential parts of a phenomenon and get to a deeper level of principles that underline it.