Extratropical cyclones are the primary source of precipitation in the mid-latitudes. The physical mechanisms that drive cyclones are well understood, and a variety of studies have demonstrated strong relationships between cloud structures and cyclone dynamics. However, past research has focused on simplistic cloud categorizations, which lack spatial and textural information that is included in more sophisticated classification schemes. Unsupervised deep learning approaches may have significant advantages over these past methods, allowing them to discover previously unidentified cloud information in large datasets. One such approach is the rotation-invariant cloud clustering (RICC), which combines a dimensionality reduction deep learning technique with rotation-invariant clustering of input cloud images. We employ the RICC, along with two established cloud clusters, to investigate the relationship between extratropical cyclones and horizontal cloud distributions. We focus on comparing these different sets of clusters to each other. First the spatial distributions and the physical properties of the identified cloud types are examined around cyclones and the results corresponding to each classification are compared in detail. Then the similarities of these distributions are quantified using structural similarity. Additionally, the evolution of spatial distributions of cloud over the lifetime of cyclones is compared between the different classifications. Interestingly, we identify the same broad physical developments in all sets of clusters. Notably, identified differences are likely due to differences in measurement processes and resolutions of the corresponding datasets.