Let's try again, slowly. A model reproduces the physical aspects of the system it is copying. Depending on how authentic it is, it will reproduce some all the physical actions. A perfect model would be identical to the thing it is modelling.
A simulation reproduces the mathematical relationships of the system it is copying. In this way, the behaviour of the system can be predicted. A perfect simulation would perfectly predict the behaviour of the system it is copying. It would not, however, ever reproduce the physical behaviour of the system.
The fact that both models and simulations actually exist in the real world does not imply that a simulation can, if sufficiently detailed, reproduce the physical behaviour of the system it is copying. Reproducing the physical behaviour is not what a simulation is for.
The difference between simulations and models is to be seen in computers, where software can be written to, say, control a power station. Often, such control software is tested by connecting it to a simulation of the power station. The control software has to be written as control software, though. A simulation of the power station controller can't just be "hooked up" to a real power station. That's not how control software works. It has to be designed from the start.
It's not uncommon for programmers designing control systems to mock up simple simulations to study the system they are controlling. It's also not unknown for non-technically-minded managers to suggest "hooking up" the simulation to the actual power plant, or water works, or space shuttle re-entry system. Such category errors can be very expensive if unrecognised.
It's also the case that models of necessity must be also simulations - if they reproduce the physical relationships, they must de facto reproduce the mathematical relationships as well. Simulations may also be models - even if the only physical attribute that they copy is the appearance, say.