While I understand what simulation and emulation mean in general, I almost always get confused about them. Assume that I create a piece of software that mimics existing hard
Simulator is something more broader than Emulator and it seems like the duality of this terms is overthought in the posts above.
Emulator
People decided to use a new word emulation in the "computer world" when they started replacing some hardware parts of the existing system in straightforward manner - imitating their behaviour and relying on the computational nature to be sure to not break something and leave everything in the equivalent state. So we have emulated the piece of this! (and the whole still works as before)
Emulator usually used in narrow sense in digital area as replacement and virtualization - presenting in digital form as a piece of software - of something known and existed before (virtual chips, circuit boards, electronic devices). So when the world became more digital and brought the emulator word to the masses, the masses added uncertainty to it (or additional reasons).
Simulator
First of all, I saw many comments about emulators do or replace something real but simulators not.
BUT flight simulator is used for a real thing - it trains pilots, gives them skill up and knowledge and it replaces expensive real planes and saves much of money. And we cannot just say a plane-emulator because we have inner feeling that this is much more than that, so we call it simulator :) Plane simulator could contain emulated radar or transponder that is true.
Contra-statements that simulators are used for analysis and study (and emulators for something real), but that analysis and study not less a real thing than emulated GSM boards (even more in the informational age we live in). Analysis adds a value to the business, cuts costs or points out to profits not less than the replaced (emulated) hardware.
Simulator is similar to modelling of something that we can't obtain for some reason (cost, technology, physical impossibility). It is usually simulated for something new or intangible or complex or not properly known to us like market, weather, combustion, user. So here comes the flight, black hole, stock exchange, simulations.
So finally:
As for words origin
All came from Latin and mean: