We could be a little more permissive here about what constitutes a "model".

    Models are not systems. <=> Maps are not territories.

Formal systems are models. They model the world. Depending on which formal system you use, one may model the world better than another. There is no "perfect" there is only "comprehensible", "insightful", and, when predicting the future, "accurate". All of these are measured in degrees, not kinds.

Models are not related to systems a priori. You are permitted to apply any model to any system. Whether the application is useful is only posterior to this first step.

To me this a problematic viewpoint. All these formalisms are not meant to be models of the world. I’d even argue for anything to be accepted as a formal system it must be far removed from taking stances on reality.

Not all formalisms are models of the world. Not all models are formalisms. But all formalisms are models.