Induced-charge separation takes place within a generator by electromagnetic induction, with electrons flowing away from one terminal and toward the other, until, in the open-circuit case, sufficient electric field builds up to make further movement unfavorable.
In charging by induction, a charge on one object with an excess of (or lack of) electrons induces an originally charge neutral object's electrons to separate and move away from one another. Then, if a ground potential path is available, those electrons will be drawn from or supplied to the separated charges, draining electrons to the ground or supplying electrons. The result then will be a net lack of or excess of electrons on the originally neutral object.
The difference is the requirement of a ground in charging induction, and that no contact is required to initiate charge separation. There is no such requirement in induced charge separation, wherein a generator, a continuous copper wire is acted on by the magnetic field to induce charge separation.