van der Waals (vdW) forces is an umbrella term for 3 (main) types of intermolecular forces:
- London dispersion forces (dispersion forces), which arise from temporary fluctuations in electron distribution within molecules, creating instantaneous dipoles.
- Debye forces, which exist between permanent dipoles and induced dipoles.
- Keesom forces, which exist between permanent molecular dipoles(also are temperature dependent).
London dispersion forces are always present, regardless of the polarity of the molecules, but they can still vary widely in strength, because of factors such as the molar mass. We say "van der Waals (vdW) forces" are shown when a combination of the above listed forces exsits, whether that is Keesom+London or Debye+London or all three(very rare). Regardless, it is always better to individually refer to them. London dispersion forces are a specific type of vdW forces, which is omnipresent, and cannot interchangeably be used with the entire category or any other forces within it.
To answer your extension: as it does not specify any electron correlation method, it can be said that most post-Hartree-Fock methods are capable of capturing specific forces within the van der Waals (vdW) umbrella. However, it is challenging for a single theory to capture all the interactions simultaneously with accuracy. First because of how negligible something as weak as London dispersion forces becomes, in the presence of a dipole-dipole interactions. Secondly, most methods excel in capturing one type of interaction with the highest accuracy. For example, dispersion-corrected DFT is effective for dispersion forces, but it may not be so for dipole-dipole interactions without additional corrections.