For a long time, I have been thinking about how a clear distinction could be made between "modeling" and "simulation." The answer to this question likely depends on the field of study. I will limit myself to the field of (computational) astrophysics. Many colleagues use "modeling" and "simulation" interchangeably, but I believe that a semantic distinction needs to be made.
For starters, "modeling" sounds less sophisticated/complicated/detailed/involved than "simulation." But this is just purely subjective. Let's go a bit beyond the sound of these words.
A good example that can help us appreciate the differences between simulation and modeling comes from gravitational wave physics: Advanced LIGO needs templates (predictions) of gravitational waves to find the same or similar waves in its data stream. Such predictions can come from detailed, approximation-free simulations that implement Einstein's equations on a computer ("numerical relativity simulations", see http://www.black-holes.org). Alternatively, they can come from so-called post-Newtonian "models" or from phenomenological "models" that try to approximate the numerical relativity simulations' results. These models are a lot simpler and computationally cheaper than full numerical relativity simulations. So that's why they find frequent use. But their results are not quite as good and reliable as the results of numerical relativity simulations.
Another useful example comes from supernova simulations and modeling of observables: It is not currently possible to simulate a core-collapse supernova explosion of a massive star end-to-end from first principles. The process involves the very last stages of core and shell burning, core collapse, core bounce, the postbounce phase during which the stalled supernova shock must be revived (all occurring within seconds of the onset of collapse), and the long-term propagation (up to days of physical time!) of the re-invigorated shock through the stellar envelope. So, on the one hand, detailed simulations are used to study the mechanism that revives the shock. But these simulations are too computationally intensive to carry out for more than a few hundred milliseconds, perhaps a second in 3D. On the other hand, simpler (often spherically-symmetric [1D]) modeling is applied to predict the propagation, breakout, and expansion of the ejecta and the resulting light curves and spectra. These explosion lightcurve/spectral models (most of the time) start with fake ad-hoc explosions put in at some mass coordinate in various ways.
Here is a slide from a talk on simulation and modeling of gravitational wave sources that I gave at a recent Instituto de Cosmologia y Fisica de las Americas (COFI) workshop in San Juan, Puerto Rico:
I think that the items listed on this slide are broadly applicable to many problems/phenomena in astrophysics that are currently tackled computationally. Ultimately, what we want is to simulate and have fully self-consistent, reliable, and predictive descriptions of astrophysical events/phenomena. This will require another generation of supercomputers and simulation codes. For now, it is a mix of simulation and modeling.