The Casimir effect and the Van der Waals force between two conducting plates are one and the same thing.
To see this, consider the boundary conditions postulated for the Casimir effect. The electric field has to be exactly zero at the plates. Because of this, it is said, the zero point energy of the vacuum is lower in between the plates than outside, which causes the interaction. But these references to the vacuum and virtual particles are mere heuristics. What does it mean for the electric field to be zero at the plates? The charges in the plate will have to redistribute and polarize the plate to generate a corresponding field.
But the interactions between fluctuating polarizations are precisely the dispersion forces that are responsible for the Van der Waals interaction.
Thus they are two explanation of the same phenomenon.