The ME was marketed as an "entry level" SLR. Its features were much like the Nikon EM -- auto exposure only, no manual mode. Price was low end. There were some other similar models such as the MV, MG, etc.
The MX was marketed as a manual-mode SLR for pros and had pro-oriented accessories such as a bulk film back, better meter, optional focusing screens, etc. The "X" in its designation was meant to position it with the LX, Pentax's flagship pro 35mm SLR at that time.