  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.
