"Vortex drag"
we all know those graphs, but that is not a very satisfactory way to explain induced drag, in my opinion. It can be elegant for math lovers, though.
Think of induced drag as "Vortex drag"
As far as I understand, induced drag and the vortex are related. Forget the infinite and finite comparison. Wing are finite, we agree in that, right?
the total aerodynamic reaction is what matters. If we divide it in two vectors (two is enough!), one at right angles with airplane's flight path and the other parallel, then we have Lift and Drag. Now, part of the total reaction paralel to the flight path is due to viscosity forces: friction drag and form drag (due to airflow separation). They are the parasite drag. Then, there is the effect of the vortex created by air "leaking" from the lower surface to the upper surface, the spanwise flow, etc... It is a physical thing, not a geometrical thing.
The drag due to vortex is the drag due to the "ability" of the wing to deflect air, which is the ability to create a pressure differential between lower and upper surfaces and it is proportional to angle of attack. The CL represents this ability. The slower you fly with the same lift, the more CL you need, the more intense the vortex, the higher the induced drag. The drag due to viscosity is due to friction, nearly independent of the angle of attack. The more air is "processed" by the wing (the more the dynamic pressure) the more the parasite drag.