The definitions of the words describe the difference the best. A google search gives the following definitions of simulate and emulate:
simulate imitate the appearance or character of.
emulate match or surpass (a person or achievement), typically by imitation.
A simulation imitates a system. An emulation simulates a system so well that it could replace it or may even surpass it.
In computing, an emulation would be a drop in replacement for the system it is emulating. Often times it will even outperform the system it is imitating. For example, game console emulators usually make improvements such as greater hardware compatibility, better performance, and improved audio/video quality.
Simulations, on the other hand, are limited by them being models. They are a best attempt to mimic a system, but not replacements for it. There are hardware emulators because hardware can be imitated and it would be hard to tell the difference. There is no Farming Emulator because there is no emulation that could replace actual farming. We can only simulate a model of farming to gain insight on how to farm better.