Yes, there are fundamental differences between the principle of an emulator and a debug module.
One of the first point is, if you use DBG on S08 for debugging, it won't be available to your application (memory window protection, code execution keyed...).
Also, I not only expect but REQUIRE an emulator to behave EXCATLY the same way as the silicon stand alone, whereas the debugger is not supposed to (there is a certain degree of intrusion).
On MMDS/MMEVS/FSICE, the only module not being used from the MCU is the Flash which is emulated by on-board RAM. Other than this, all modules used are the one from the MCU.
Just to compare to S12: both emulators and BDM tools are available. Of course emulators are much more expensive.
Alban.