  Numerous metrics exist to quantify the dynamical state of galaxy clusters,
both observationally and within simulations. Many of these correlate strongly
with one another, but it is not clear whether all of these measures probe the
same intrinsic properties. In this work, we use two different statistical
approaches -- principal component analysis (PCA) and uniform manifold
approximation and projection (UMAP) -- to investigate which dynamical
properties of a cluster are in fact the best descriptors of its dynamical
state. We use measurements taken directly from The Three Hundred suite of
galaxy cluster simulations, as well as morphological properties calculated
using mock X-ray and SZ maps of the same simulated clusters. We find that four
descriptions of dynamical state naturally arise, and although correlations
exist between these, a given cluster can be "dynamically relaxed" according to
all, none, or some of these four descriptions. These results demonstrate that
it is highly important for future observational and theoretical studies to
consider in which sense clusters are dynamically relaxed. Cluster dynamical
states are complex and multi-dimensional, and so it is not meaningful to
classify them simply as "relaxed" and "unrelaxed" based on a single linear
scale.
