The distintion between the two terms is a bit fuzzy. Coming from a world where "Emulators" are pieces of hardware that allow you debug embedded systems. And remember products that allowed you to have ICE (In Circuit Emulation) capabilities to debug a PC platform, I find the use of the term "Emulation" to be a somewhat of a misnomer for software that SIMULATES the behaviour of a piece of hardware.
My justification for the current use of the term is Emulation is that it may "augment" the functionality, and only is concerned with a "reasonable" approximation of the behaviour of the system.
ICE: (In Circuit Emulation)
A piece of hardware that is plugged into a board in place of the actual processor. It allows you to run the system as if the actual processor was present. Typically these have a variant of the processor on them to actually execute the software with glue logic to allow the user to break executation and single step under hardware control. Some would also provide logging capability. Most modern processors development systems have replace ICE type emulation with JTAG Emulation, where the JTAG just talks to the processor via a special purpose serial link and all execution is perform by the processor mounted on the board.
Software EMULATOR:
An 0x86 emulator is only concerned with being able to execute 0x86 assembly language, not providing accurate cycle per cycle behaviourial model of a SPECIFIC 0x86 processor. Bochs is an example of this. QEMU does this, but also allows "virtualization" using special kernel modules.
SIMULATOR:
Texas Instruments provides a CYCLE ACCURATE behaviourial model of there processors for software development that is intended to be a accurate SIMULATION of SPECIFIC processor cores behavior for the developers to use prior to having working hardware.
Software EMULATOR augmenting functionality:
BLEEM not only allowed you to run Playstation Software, but also allowed the display to be output with higher resolution than the Playstation was able to provide, and also took advantage of more advanced capabilities of GPUs that were avaliable. (i.e. Better blending and smoothing of textures.)