Dear Student ,
Electromagnetic Induction :: When the current flowing through a circuit is started or stopped or changed by then it is observed that other currents are set up in all the other closed circuits which are near the first one .
Mutual Induction :: When the circuits are not closed the tendency to produce a current is present just the same but being open circuits no currents results .If a current in second circuit is varying there will be a corresponding emf induced in the first circuit .
Regards