  The main goals of the present work are (i) to study the substructure content
of a representative, X-ray selected sample of 31 galaxy clusters, as traced by
the spatial distribution of their red-sequence galaxies, and (ii) to compare it
to that observed in the intracluster medium distribution. Our substructure
indicators are the asymmetry test, $\beta$, the residuals of the galaxy surface
density map, $\Delta_\Sigma$, and the Fourier elongation, $FE$. We probe the
clusters core with secondary tests: the offset between the central brightest
cluster galaxy and the X-ray emission peak, $\Delta r_{\mathrm{BCG-X}}$, the
magnitude offset between the first and second brightest galaxies, $\Delta
m_{12}$, and their radial offset, $\Delta r_{12}$. The main indicators exhibit
continuous distributions, making a discrete classification difficult. A
partition based on $\beta$ and $\Delta_\Sigma$ gives a fraction $\sim35\%$ of
disturbed systems; $\sim65\%$ of the clusters are disturbed according to at
least one of these two quantities. The main indicators poorly correlate with
the secondary quantities, likely due to substructures observed prior core
crossing. Nine of the 12 X-ray disturbed clusters are also flagged as such by
either $\beta$ or $\Delta_\Sigma$. Cool cores are hosted by systems with higher
optical concentrations, smaller $\Delta r_{\mathrm{BCG-X}}$, and larger $\Delta
r_{12}$; however, both populations do not differ significantly in terms of
their overall morphology probed by the main indicators. Our results show the
necessity of using a variety of independent tests and data sets to obtain a
clear picture of a cluster's morphology. Furthermore, we find that a cluster's
dynamical state, consequence of its recent merger history, is not necessarily
representative of a future mass assembly via accretion of substructures.
