The SARS-CoV-2 is the third coronavirus in addition to SARS-CoV and MERS-CoV that causes severe respiratory syndrome in humans. All of them likely crossed the interspecific barrier between animals and humans and are of zoonotic origin, respectively. The origin and evolution of viruses and their phylogenetic relationships are of great importance for study of their pathogenicity and development of antiviral drugs and vaccines. The main objective of the presented study was to compare two methods for identifying relationships between coronavirus genomes: phylogenetic one based on the whole genome alignment followed by molecular phylogenetic tree inference and alignment-free clustering of triplet frequencies, respectively, using 69 coronavirus genomes selected from two public databases. Both approaches resulted in well-resolved robust classifications. In general, the clusters identified by the first approach were in good agreement with the classes identified by the second using K-means and the elastic map method, but not always, which still needs to be explained. Both approaches demonstrated also a significant divergence of genomes on a taxonomic level, but there was less correspondence between genomes regarding the types of diseases they caused, which may be due to the individual characteristics of the host. This research showed that alignment-free methods are efficient in combination with alignment-based methods. They have a significant advantage in computational complexity and provide valuable additional alternative information on the genomes relationships.