Well, you have generalized the word "theory" quite a bit to get this "used in the same sense" result. Generalize enough and a word can mean anything, y'know. ;-)
Throughout this conversation we had been implicitly using the word "theory" in contexts where it was understood that "theories" can be proven false. See, it is not how they are developed that I see as the key difference, I suppose.
It is the fact that a "scientific theory" may be disproved, or at least proven incomplete; it is always tentative and pending further results. A "mathematical theory" if you want to call it that is always completely 100% flat-out true. Nothing can "prove it wrong". Ever!
That is the key difference because it means that Doctor Stochastic was comparing apples and oranges when he brought up "mathematical theories". They can't be "wrong" in the first place. Best,
Perhaps it's the fact that I'm an experimentalist, but I still don't see the difference. A mathematician considers a theory "right" if only it is self-consistent. By contrast, "right" or "wrong" for a scientific theory also addresses the question of whether or not it applies to the real world. But I can also apply the same standards to mathematical theorems: an experimental test of Euclid's theorems shows that they don't apply to real spaces as well as Riemann's do. To me, Riemann is "right" where Euclid is "wrong". Apples to apples, you understand.
So you see, it isn't that the word "theory" is used differently in mathematics and physics, but that the standards of "right" and "wrong" are different.
This is conceptually incorrect regarding a mathematical "theory". "Proving" a mathematical theory simply establishes that it is consistent with the assumptions of the established framework of discussion; it says nothing about whether or not it is true in any sense of the word.