The atomic motions responsible for features seen in the spectra of network-forming liquids above the relaxational frequency domain are conventionally described as vibrational, with the nature of the vibrational modes described either as local vibrations of the tetrahedral units of the network or as extended, phonon-like vibrations, depending on the standpoint of the observer. The validity of these apparently conflicting pictures of the atomic motions is examined by an instantaneous normal mode (INM) analysis of the network-forming liquid ZnCl2. Projections of the INM eigenvectors onto the idealized modes provides a way of quantifying the relationship between the actual and idealized modes. It is shown that individual INMs do not remotely conform to the modes envisaged in the simple pictures. Nevertheless, at the more coarse-grained level of identifying contributions to the density of states, the simple pictures do provide a qualitative guide to the character of the features which are observed. These findings apply to the modes calculated with several different models of the interactions, and appear to be fairly general. A detailed examination of the nature of the INMs which appear in the frequency domain of the boson peak observed in ZnCl2 is carried out and it is shown that these modes have a mixed acoustic wave and local torsional character.