The character of optical excitations in nanoscale and atomic-scale materials is often strongly mixed, having contributions from both single-particle transitions and collective, plasmon-like response. This complicates the quantum description of these excitations, because there is no clear way to define their quantization. To move toward a quantum theory for these optical excitations, they must first be characterized so that single-particle-like and collective, plasmon-like excitations can be identified. We show that time-dependent density functional theory can be used to make that characterization if both the charge densities induced by the excitation and the transitions that make up the excitation are analyzed. Density functional theory predicts that single-particle-like and collective excitations can coexist. Exact calculations for small nanosystems predict that single-particle excitations evolve into collective excitations as the electron-electron interaction is turned on with no indication that they coexist. These different predictions present a challenge that must be resolved to develop an understanding for quantum excitations in nanoplasmonic materials.