You're almost right. The induced electromotive force due to external magnetic field is proportional to rate of change of magnetic flux through the circuit. In case of the coil moving in a uniform field, the flux through it (proportional to the number of turns) does not change in time. In case of the wire, the flux changes, since the circuit's area grows or shrinks.
So many ways to be confused... I will try to tell you how I think about these things.
When I have a coil (one turn, N turns...), and I try to change the magnetic field through the area that the coil surrounds, then I have to have lines of B field "cross" the wires into the area. This may not be a scientifically accurate way to think of it, but it's very helpful for your intuition - because a B line crossing the wire is a bit like the charges inside the wire having a velocity relative to the B field, and it results in a force on the charge and therefore EMF. The more turns I have, the more charge feels the force, therefore the greater the EMF. Similarly, the larger the area, the more B lines have to cross the wire to fill the area with a certain density of lines - again, emf scales with area (or total flux).
So far so good - this is just an intuitive way to think about induction.
Now we add "flux linking". In general, if "flux in A" $\implies$ "flux in B", then we say the two are "linked" (and incidentally, it always means the reverse is also true by something call reciprocity: that is, flux in B will then always imply flux in A). The amount (strength) of the relationship is the linkage. That is,
linking = there is a relationship between $\phi_A$ and $\phi_b$
linkage = how much linking there is
I hope this confused you less, not more, than your revision guide.
Best Answer
If you consider a constant current flowing in your coil as you rotate it, you will see it at first rotating clockwise, then, after the 180 degree flip, anticlockwise.
If you create the same change in flux, but flip the coil, then you will induce a current in the opposite direction in the frame of the coil. In other words, while it will still look "clockwise" if you look at the coil from a distance, if you had painted little arrows on the coil you would see that in one instance the current flows in the direction of the arrows, and in the other instance flows against it.