Full Idea
The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it.
Gist of Idea
Models in model theory are structures, not sets of descriptions
Source
Wilfrid Hodges (Model Theory [2005], 5)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.12
A Reaction
Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things,