Comment by bityard
There is LOADS of gray area, overlap, and room for one's own philosophical interpretation... But typically simulators attempt to reproduce the details of how a particular machine worked for academic or engineering purposes, while emulators are concerned mainly with only getting the desired output. (Everything else being an implementation detail.)
E.g. since the MAME project considers itself living documentation of arcade hardware, it would be more properly classified as a simulator. While the goal of most other video game emulators is just to play the games.