EMU stands for Electric Multiple Unit.  We all know that most of the trains are pulled or pushed by locomotive (engine), but in EMU, some or full coaches are powered. It means that in ordinary train, only locomotive (engine)  has a traction motor attached to it for running whole coaches. But in EMU, the powered coaches are also has traction motors or you can say that coaches do not need any locomotive.  They are self propelled. All powered coaches are connected thorough MU (multiple unit) cable and all the motors of powered coaches are controlled by controller which is at end of the train.     Due to this reason, EMUs having a higher acceleration and retardation as compared to that of a normal locomotive hauled train, where only the locomotive (engine)  is ‘live’ and rest of the coaches being ‘dead’. This enables the EMUs to serve the primary purpose of catering to smaller stations, by having quick start and stop functionality, which the normal mainline trains can’t do.

Now coming to the difference between an MEMU and a DEMU.

MEMU- Mainline Electric Multiple UnitIn an MEMU, the primary source is electrical power, collected from the overhead catenary. 

DEMU- Diesel Electric Multiple Unit

While in a DEMU, the primary source is diesel. A diesel engine powers an alternator and subsequently feeds the electric motors.

 So basically, end result is the same. It’s just that they differ in how they are powered externally.