Using coarse-grained molecular dynamics simulations we present a comparison between the structure of an ionic liquid (IL) and its neutral counterpart (a mixture of the same molecules at the same density, but without charges). We show that there is a surprising structural similarity between the two studied systems with respect to the packing of the molecules, regardless of the fact that the arrangement of anions and cations in the ionic liquid differs significantly from the arrangement of their analogues in the neutral mixture. Rather similar behavior was obtained for the computed total (all-grain) radial distribution functions of the entire systems, as well as for the sizes and shapes of the local voids defined by Delaunay simplices. This structural similarity was also observed for an IL with a modified charge distribution on the cations, and for an uncharged Lennard-Jones liquid, both at the same density. We would like to emphasize that the overall structure of a dense disordered molecular system is determined, above all, by the impenetrability of atoms, i.e. by the geometric laws of atomic packings.