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]...
