My current interpretation is the Van Der Walls force is actually two things; 1) particle interaction via intermolecular forces such as London forces, and 2) effects from virtual modes (aka virtual particles, aka zero-point energy, aka vacuum energy, etc.) which some people appear to be very skeptical about, however, none the less these appear to be accepted in the literature at a high level, and also appear to explain various physical phenomena.
So despite the fact that all of these interactions occur on the scale of microns or less, the distance between surfaces, as well as the chemical composition of the surfaces appears to play a role in anticipating which of these forces dominates. What I am currently calling the 'Casimir force' essentially exclusively is due to actions of virtual modes; the van der walls force, I think, involves this also, but also can include other things, and is more dominant at very small distances, like nanometers.