To my understanding, a model in Model Theory is an interpretation (in a form of a set or other algebraic structures) for a certain sentence S which makes S true.
In everyday language, and also in other branches of science (physics, computer science, biology, ...), model means a formal language used to give an abstract description of phenomena, highlighting only the details we care about for the current analysis.
So, how do these two concepts relate to each other? Since we use the same word, I figured that there may be a connection which could make my understanding of these concepts deeper. In particular, I wonder why we use the world "model" in the "common sense" instead of language, abstract language, formalism, etc.