  We investigate the statistical properties and the origin of the scatter
within the spatially resolved surface brightness profiles of the CHEX-MATE
sample, formed by 118 galaxy clusters selected via the SZ effect. These objects
have been drawn from the Planck SZ catalogue and cover a wide range of masses,
M$_{500}=[2-15] \times 10^{14} $M$_{\odot}$, and redshift, z=[0.05,0.6]. We
derived the surface brightness and emission measure profiles and determined the
statistical properties of the full sample. We found that there is a critical
scale, R$\sim 0.4 R_{500}$, within which morphologically relaxed and disturbed
object profiles diverge. The median of each sub-sample differs by a factor of
$\sim 10$ at $0.05\,R_{500}$. There are no significant differences between
mass- and redshift-selected sub-samples once proper scaling is applied. We
compare CHEX-MATE with a sample of 115 clusters drawn from the The Three
Hundred suite of cosmological simulations. We found that simulated emission
measure profiles are systematically steeper than those of observations. For the
first time, the simulations were used to break down the components causing the
scatter between the profiles. We investigated the behaviour of the scatter due
to object-by-object variation. We found that the high scatter, approximately
110%, at $R<0.4R_{500}$ is due to a genuine difference between the distribution
of the gas in the core. The intermediate scale, $R_{500} =[0.4-0.8]$, is
characterised by the minimum value of the scatter on the order of 0.56,
indicating a region where cluster profiles are the closest to the self-similar
regime. Larger scales are characterised by increasing scatter due to the
complex spatial distribution of the gas. Also for the first time, we verify
that the scatter due to projection effects is smaller than the scatter due to
genuine object-by-object variation in all the considered scales. [abridged]
