MAE was Apple's fascinating attempt to run Mac OS on Unix workstations, essentially creating a compatibility layer that translated Mac Toolbox calls to X11, allowing Unix users to run Mac software without actual Apple hardware.
It was essentially a reverse-engineered MacOS Rom Toolkit. It implemented most of System 7 as well as QuickDraw.
http://preserve.mactech.com/articles/mactech/Vol.13/13.06/Ju...
There are also differences at the level they execute: MAE can, and was designed to run, as an independent process like any other well-behaved X11 application, and multiple users can run multiple sessions of it, but Classic/Blue Box needs operating system support and only one instance of it can be running on a system by a single user.