I do not know whether this is the general opinion, but I've always differentiated the two by what they are used for. An emulator is used if you actually want to use the emulated machine for its output. A simulator, on the other hand, is for when you want to study the simulated machine or test its behaviour.
For example, if you want to write some state machine logic in your application (which is running on a general purpose CPU), you write a small state machine emulator. If you want to study the efficiency or viability of a state machine for a particular problem, you write a simulator.