Consider the following two cases,
Case 1 – A coil moving through a constant magnetic field
Now, in Case 1 (a coil moving through a constant magnetic field) the induced current is zero, whilst in case 2, there is an induced EMF.
Is the reason that there is no induced current in case 1 because current gets induced equally on either side of the coil and it therefore cancels out. This would be concordant with case 2, as in case 2 a conductor likewise moves through a constant magnetic field and is able to induce an EMF.
Is the reason that there is no induced current in case 1 because there is no change in flux. This appears to not be in line with case 2, as in case to, there is likewise 'no change in flux' but an EMF is induced.