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I'm not sure there's a meaningful difference (between "theory" and "doctrine"), or perhaps not one which every agrees on.
Per Google these seem to be used with the same frequency/popularity:
It's never called a "theory of two truths" though.
If you use the Ngram viewer (which I think only searches books), then "doctrine of emptiness" is the more popular.
So published (book) authors tend to call it a doctrine.
As an aside -- not about Buddhism but about the way the word "theory" is used in English -- the word "theory" isn't necessarily pejorative (e.g. meaning "speculative , unproven, and wrong"): especially when scientists used that word.
For example it tends to be called "Einstein's Theory of Relativity", not because that's wrong or unproven, but apparently because it's an explanation (perhaps even akin to a doctrine) not just an observation.
This seems plausible to me -- When will Einstein's theory of relativity become a law of relativity? -- i.e. consistent with how physicists might use the term.
See also Laws and theories explained on Physics.SE.
Also note that e.g. Newton's laws are merely "excellent approximations at the scales and speeds of everyday life" (i.e. non-relativistic) -- a "law" needn't be "more true" than a "theory".
But the shades of meaning are a bit subtle, perhaps you can't infer much about why people might use or the other.
Certainly "doctrine" though, anyway, right?
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A Theory may refer to any group of hypothesis or facts used to explain some aspect of nature.
The concept of Doctrine may overlap with the definition of theory, with the difference that the former might contain some prescriptive ideas or principles to guide some actions. In your question, the Doctrine of Two Truths might understood as a guide to study the Dharma, telling you how to interpret some of the teachings.
Kind regards!