The rectangular loop in the problem has a cut as shown in the diagram above.  The cut causes charge separation and a potential gets developed between the cut ends.

When the cut is not present, it will be a closed loop and not much of charge separation happens as in above case.

Even a small wire moved quickly in a magnetic field, develops induced emf. The ends of the wire develop potential difference due to charge accumulation. This is the same reason why we have different kinds of coil in electromagnetic induction.