Eddy currents on a conductors surface, and induced current flow around the loop both coexist? The title seems confusing, because Eddy currents are induced currents... however, let me explain.
Assume the following closed loop passing a uniform magnetic field like so:

Now, this loop would have an induce EMF to allow current flow to oppose the change that induced it like so:

Are there Eddy currents induced as well on the surface? 
Vs this diagram(closer look into that portion of the wire):

My confusion lies with Eddy currents on the surface, or just induced current that circulates around the loop opposing the change that induced it... can both coexist?
 A: The physics creating eddy currents and EMFs in inductors is the same: Faraday's law of induction. 
$ \oint_C {E \cdot d\ell = - \frac{d}{{dt}}} \int_S {B_n dA} $
The strength of any induced current and voltage is dependent on:
1) The amount of magnetic flux ($\int_S {B_n dA}$)
2) The rate at which the flux is changing
So for the loop in your first picture, lets assign some dimensions. We'll call the outer radius $ R $ and the inner radius $ r $ so that the thickness of the ring is $R-r$. For a very small thickness, clearly the amount of flux through the ring will be >> than the magnetic field hitting the conductor at any given time. So left side of faraday's law will be much larger for the circuit of the entire loop than for the that of the loop drawn on the conductor. 
Moreover, the left side of the equation indicates an induced voltage, so the current generated is proportional the resistance. Eddy currents are primarily on the surface of the conductor (this is why they are often used for non-destructive testing of materials to find cracks on the surface of sheet metal). So the resistance seen by the eddy currents I believe would be much larger than the resistance seen by the currents in the ring as the A in:
$ R = \rho L/A $
Would be much larger for the current induced around the loop.
In conclusion, both can exist (and can oppose each other), and certainly do in your example, typically the induced current in the loop is just dominant for any well designed inductor. In brakes that utilize the drag induced by eddy currents, one would design for the opposite effect. 
