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Context. This is the second work dedicated to the observed parallelismbetween galaxy clusters and early-type galaxies. The focus is on thedistribution of these systems in the scaling relations (SRs) observed wheneffective radii, effective surface brightness, total luminosities and velocitydispersions are mutually correlated. Aims. Using the data of the Illustrissimulation we try to speculate on the origin of the observed SRs. Methods. Wecompare the observational SRs extracted from the database of the WIde-fieldNearby Galaxy-cluster Survey (WINGS) with the relevant parameters coming fromthe Illustris simulations. Then we use the simulated data at different redshiftto infer the evolution of the SRs. Results. The comparison demonstrate thatgalaxy clusters (GCs) at z~0 follow the same log(L)-log(sigma) relation ofearly-type galaxies (ETGs) and that both in the log(Ie)-log(Re) andlog(Re)-log(M*) planes the distribution of GCs is along the sequence defined bythe brightest and massive early-type galaxies (BCGs). The Illustris simulationreproduces the tails of the massive galaxies visible both in thelog(Ie)-log(Re) and log(Re)-log(M*) planes, but fail to give the correctestimate of the effective radii of the dwarf galaxies that appear too large andthose of GCs that are too small. The evolution of the SRs up to z=4 permits toreveal the complex evolutionary paths of galaxies in the SRs and indicate thatthe line marking the Zone of Exclusion (ZoE), visible both in thelog(Ie)-log(Re) and log(Re)-log(M*) planes, is the trend followed by virializedand passively evolving systems. Conclusions. We speculate that the observed SRsoriginate from the intersection of the virial theorem and a relation L=L_0 xsigma^beta where the luminosities depend on the star formation history.

The parallelism between galaxy clusters and early-type galaxies: II. Clues on the origin of the scaling relations