The multihadron production in nucleus-nucleus collisions and its interrelation with that in (anti)proton-proton interactions are studied by exploring the charged particle mean multiplicity collision-energy and centrality dependencies in the measurements to date. The study is performed in the framework of the recently proposed effective-energy approach which, under the proper scaling of the collision energy, combines the constituent quark picture with Landau relativistic hydrodynamics counting for the centrality-defined effective energy of participants and relating different types of collisions. Within this approach, the multiplicity energy dependence and the pseudorapidity spectra from the most central nuclear collisions are well reproduced. The study of the multiplicity centrality dependence reveals a new scaling between the measured pseudorapidity spectra and the calculations. By means of this scaling, called the energy balanced limiting fragmentation scaling, one reproduces the pseudorapidity spectra for all centralities. The scaling elucidates some differences in the multiplicity and midrapidity density centrality dependence obtained at RHIC and LHC. These findings reveal an inherent similarity in the multiplicity energy dependence from the most central collisions and centrality data. A new regime in heavy-ion collisions to occur at about a TeV energy is indicated, similar to that observed in the earlier studies of the midrapidity densities. Predictions are made for the mean multiplicities to be measured in proton-proton and heavy-ion collisions at the LHC.