This entire question is a case of classical equivocation.

Theories in sciences don't have axioms.  In fact theory, in the sense of Set Theory, or The Theory of Complex Variables has nothing in common with the notion of a scientific theory whatsoever.

A scientific theory is a proposed explanation for a set of phenomena, and a theory in the mathematical sense does not explain anything, it is a subject in itself.

In math, a theory is a major part of a field of study that is somewhat separable from related parts of the same field.  It is often defined as the body that proceeds from the understanding of a given model.

The modern way of looking at a model is as the embodiment of a set of axioms.  But that is not the only approach to take.  A lot of people do not think of Euclidean geometry as what proceeds from Euclid's axioms, but what proceeds from a given shared understanding that humans develop naturally by living in macroscopic three-dimensional space.  So by that notion, things like geometry, real analysis and number theory do not really involve axioms.  The axioms are created to solidify our understanding, but they are in some sense superfluous, and a concession to a level of excessive modern formalism in logic, and to the success of abstract algebra.  These domains that focus intently on a single model really have that model in a more informal, but shared set of ideas.

So:

  1. These two things don't really overlap.

  2. Even in math, axioms are only an aspect of a given approach, although an extremely common one.