Final answer:
The vast hierarchy that organizes every creature's relationship to others is known as the taxonomic classification system, created by Carl Linnaeus. This system groups organisms into a series of increasingly specific categories, from domains down to species.
Step-by-step explanation:
The vast hierarchy that explains every creature's relationship to all others is known as the taxonomic classification system. This hierarchical model, developed by Carl Linnaeus, organizes the incredible diversity of life into a framework that groups organisms based on shared characteristics. The hierarchy begins with three broad categories called domains: Bacteria, Archaea, and Eukarya. Within each domain, life is further categorized into a kingdom, followed by the subsequent levels of phylum, class, order, family, genus, and species, with each level representing a more specific grouping.