The role of interlayer bonds in the two-dimensional (2D) materials "beyond graphene" and so-called van der Waals heterostructures is vital, and understanding the nature of these bonds in terms of strength and type is essential due to a wide range of their prospective technological applications. However, this issue has not yet been properly addressed in the previous investigations devoted to 2D materials. In our work, by using first-principles calculations we perform a systematic study of the interlayer bonds and charge redistribution of several representative 2D materials that are traditionally referred to as van der Waals systems. Our results demonstrate that one can distinguish three main types of interlayer couplings in the considered 2D structures: one-atom-thick membranes bonded by London dispersion forces (graphene, hBN), systems with leading electrostatic interaction between layers (diselenides, InSe, and bilayer silica), and materials with so-called dative or coordination chemical bonds between layers (ditelurides). We also propose a protocol for recognizing the leading type of interlayer bonds in a system that includes a comparison of interlayer distances, binding energies, and the redistribution of the charge densities in interlayer space. Such an approach is computationally cheap and can be used to further predict the chemical and physical properties, such as charge density waves (CDW), work function, and chemical stability at ambient conditions.