This is a good question with a complex answer. Different models are created with different purposes in mind. As an example, there are qualitative and quantitative models. Qualitative models sacrifice some realism to demonstrate a particular phenomenon in the clearest way possible. Quantitative models sacrifice this clarity to create something more empirically relevant.
I once came across this sentence in a paper and I like the way they phrased it:
It's from "Optimal Environmental Taxation in the presence of other taxes: General-equilibrium analyses" by Bovenberg and Goulder:
The use of a numerical model enables us to employ a realistic
specification of taxes and adopt a fairly detailed representation of
production and demand. Our paper thus combines the strength of
analytical and numerical approaches: a stylized analytical model
uncovers the major mechanisms at play, while a numerical model
explores the empirical significance of these mechanisms in a more
realistic setting. Despite considerable differences in the complexity
of the analytical an numerical models, we find a strong coherence
between the two model's results.
there are some models that are purely statistical.
There are also some models that are built solely for prediction. In short, there are many more types of models with different purposes. A model should be judged on its purpose.
Also, as for uncovering "the truth." You might consider reading more about causal inference. This is one of the most important parts of econometrics. For starters, read about the method of Instrumental Variables. There are several other questions and answers on this website that deal with this.