Both means something doing the job of something else.
The difference is that "Simulation" happens at a conscious level (respectowith respect to the user) and is finalized typically to anticipate the result of a reality without touching the reality itself.
"Emultaion""Emulation" happens at an unconscious level, and has the purpose to replace an underlying component with another different one that -in respect to the user- works as the old one.
In other words, simulation happen in a "parallel world", while emulation happens in a "replaced world".