= Taxonomic rank
A <taxonomic rank> is a named level in a biological classification hierarchy. <Taxonomic order>, <taxonomic family>, <genus (biology)> and <species> are ranks; <Carnivora> is a <taxon> at order rank, and <Felidae> is a <taxon> at family rank. A rank answers what level a group occupies, while a taxon identifies which group is meant.<Biology 2e by Mary Ann Clark and others>[section 20.1, Classification Levels]{ref}
In a simplified nested classification, let $S$, $G$, $F$ and $O$ be the organism sets belonging to one species, its genus, its family and its order. Then $S\subseteq G\subseteq F\subseteq O$. The subset symbol expresses inclusion, not equality of the number of members or a fixed numerical spacing between levels.
For instance, a hypothetical family can contain one genus with ten species, whereas another family contains five genera with two species each. Both have ten species and occupy the same rank, yet their internal grouping differs. Rank, species count and genus count are distinct data.
Nor must each biological <clade> receive a traditional rank: a <phylogenetic tree> can resolve many branching groups between two named levels. The hierarchy provides a practical naming framework, while the evolutionary hypothesis contains additional structure.<Biology 2e by Mary Ann Clark and others>[section 20.1, phylogenetic trees and classification]{ref}
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