Using the catalogues of galaxy clusters from The Three Hundred project, modelled with both hydrodynamic simulations, (Gadget-X and Gadget-MUSIC), and semi-analytic models (SAMs), we study the scatter and self-similarity of the profiles and distributions of the baryonic components of the clusters: the stellar and gas mass, metallicity, the stellar age, gas temperature, and the (specific) star formation rate. Through comparisons with observational results, we find that the shape and the scatter of the gas density profiles matches well the observed trends including the reduced scatter at large radii which is a signature of self-similarity suggested in previous studies. One of our simulated sets, Gadget-X, reproduces well the shape of the observed temperature profile, while Gadget-MUSIC has a higher and flatter profile in the cluster centre and a lower and steeper profile at large radii. The gas metallicity profiles from both simulation sets, despite following the observed trend, have a relatively lower normalisation. The cumulative stellar density profiles from SAMs are in better agreement with the observed result than both hydrodynamic simulations which show relatively higher profiles. The scatter in these physical profiles, especially in the cluster centre region, shows a dependence on the cluster dynamical state and on the cool-core/non-cool-core dichotomy. The stellar age, metallicity and (s)SFR show very large scatter, which are then presented in 2D maps. We also do not find any clear radial dependence of these properties. However, the brightest central galaxies have distinguishable features compared to the properties of the satellite galaxies.
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