The answer is that there is one (or perhaps two) types of bonds. A bond occurs when two atoms are attracted in a net-electrostatically favorable way. (Of course, the electrons and protons are subject to their quantum nature)
Why two? In the Quantum Theory of Atoms in Molecules, the "procedure" is:
- Ascertain whether a bond path exists between two atoms (atomic basins). This is a yes/no answer -- the is a bond or no bond -- because it is electrostatically favorable or unfavorable.
- If a bond path does exist, then the sign of the Laplacian of the electron density at the bond critical point tells you whether the interaction is "covalent" or "not covalent" though these terms are not strictly applicable. +/- yeilds only TWO possible types of bonds.
BTW: The Laplacian of any field is a measure of whether the electron density at a particular point is a "sink" or a "source." The reality is: there is an entire, continuous spectrum of values of the Laplacian. None of them present themselves as being called "dipole" or "van der Waals"
In summary, there is one language of bonding, and that is couched in Quantum Physics. You will never hear of van der Waals forces in a physics [quantum electrodynamics] class, because there is no such thing. There is no van der Waals term in the Schroedinger equation.
The difference between chemical and physical bonds as taught in class is simple: chemistry as a whole has not shaken the pre-quantum revolution description of a bond. It is disastrously complicated for students and professionals in the field, as there is a never ending squabble as to whether something is a "dipole-dipole" or "dipole-induced dipole" or "three center, two electron" But these are all arguments built on shaky scaffolding.
The fact is that the rules of physical bonding are almost "boring." The second fact is that most bond descriptions in chemistry have only certain elements of reality. To the credit of chemists, they need to quickly and efficiently describe certain oft-appearing motifs in bonding--without resorting to a quantum chemistry calculation--and they have done a pretty good job. It's just that these descriptions are somewhat ambigious and always open to interpretation, hence not purely quantum mechanical.