In my reading of Alfred Tarski's model theory, a theory is a formal system whose sentences are without inherent meaning, but which becomes meaningful (e.g. having truth values) only after a model provides an interpretation of its sentences as referring to anything in which some notion of truth may obtain, such as the structure of the empirical world.
On the other hand a colloquial model, has an inherent structure all its own, such as a "model car" or some other structure which may be interpreted as referring to a truth-bearing structure, e.g. an actual car. Indeed, this quote taken from Julian Jaynes's "The Origin of Consciousness in the Breakdown of the Bicameral Mind" comports with this understanding of model, and goes further to refer to theory as the interpretation:
The Bohr model of the atom is that of a proton surrounded by orbiting electrons. It is something like the pattern of the solar system, and that is indeed one of its metaphoric sources. Bohr’s theory was that all atoms were similar to his model. The theory, with the more recent discovery of new particles and complicated interatomic relationships, has turned out not to be true. But the model remains. A model is neither true nor false only the theory of its similarity to what it represents.
The sincere investigator of truth might become befuddled by Tarski's seemingly reversed meanings from that in common use -- confused to the point that meta-understanding is subverted, as "understanding" is further described by Jaynes:
A theory is thus a metaphor between a model and data. And understanding in science is the feeling of similarity between complicated data and a familiar model.
Tarski was no lightweight so we are left with a rather urgent question regarding this befuddlement:
What is it about colloquial meta-understanding that is so wrong-headed regarding empirical reality that Tarski sought to reverse the meanings of these words OR what is it about my understanding of Tarski (and/or Jaynes and/or colloquial usage) that renders Tarski's meanings consilient with the colloquial?