As someone with a degree in physics and math, I find the line you're trying to draw rather blurry.

> Quantum physics is a theory, as in "as far as we can tell, this is an exact mathematical description of the world".

Is it?

If by "mathematical exactness" you merely mean we have somehow been able to produce some numbers that later on we measured in experiments, then yes. (Though we haven't been able to produce such numbers in all cases, see e.g. [0].)

I my book, though, mathematical exactness means your model is mathematically consistent and is applied with the necessary mathematical rigor.

Quantum mechanics and quantum field theory, as they are commonly taught in universities, are everything but. They are a bunch of concepts and recipes that, albeit successful, are held together loosely with duct tape and lots of hand waving to make you ignore the logical gaps & jumps and the fact that many of the "mathematical" objects physicists refer to don't even exist[1]!

[0]: https://www.scientificamerican.com/article/this-simple-exper...

[1]: Haag's Theorem, Aizenman–Fröhlich Triviality Theorem, etc.

I’m not sure most physicists would make that specific distinction between "theory" and "model". We know QM is wrong or at the very least incomplete as long as there’s no theory of quantum gravity. Every theory, like every model, has a domain of applicability and gives wrong or even nonsensical answers when applied outside its domain.

What a theory is, is more like a model (or maybe meta-model) with a particularly broad scope or high explanatory value, often a mathematical framework that gives a common foundation and theoretical justification for multiple experimentally-derived models.

This is an important distinction. Quantum mechanics as a framework is the correct description of reality as far as we can measure (excluding some loopholes like superdeterminism). This is as close to the foundation or "god" or whatever you want to call it as it gets. If you look at specific quantum model descriptions (like the Schrödinger equation), we know they are not complete. Even relativistically correct Dirac equation is still not the full picture, because we don't fully understand how gravity fits into this on short length scales. But the current principles like Bell's theorem exist independently with all their implications on our reality and they will not go away, no matter what else we discover at the bottom.

>>>Quantum physics is a theory, as in "as far as we can tell, this is an exact mathematical description of the world".

... which "we think" is functioning that way not to mention that theory itself might be wrong and be replaced as most of the supporters of quantum theory doesn't seem to look on it as something that explain mechanics of it, but rather how magic of "unexplainable" quantum mechanics works.

Eh I would disagree on such a sharp distinction. Both quantum mechanics and general relativity are theories, and we know that both of them are not accurate descriptions at all scales.

Heck your descriptions of a model is also what we would call an effective theory (i.e. a description valid for a specific range of parameters/scale).

I don't think there's a commonly agreed difference between model and theory and I sure have heard many physicists use them interchangeably when it suits them (and I'm guilty of it myself). Perhaps theory feels 'wider', as in quantum theory encompasses models for many quantum systems, but that's as far as I'd go.