Class, category, genus, species, denomination, genre are compared here only in their general, nonspecialized use, and the following comments may be inapplicable to such technical fields as philosophy and the sciences.
Class is a very general term for a group including all individuals with a common characteristic.
Class consistently implies division which may involve abstraction of a single group from a greater unclassified mass or the separation of a larger group into discrete subgroups; the basis of such a division may be strictly logical or a mere matter of convenience, and often it involves a value judgment.
Category may be interchangeable with class but is sometimes more precise in suggesting classification or grouping on the basis of a certain readily perceived criterion or on a predication, often an explicit one.
Genus and species, scientific in their suggestion, differ in that the first implies a larger less specific group, the latter a smaller more specific one.
Denomination usually indicates that the group under consideration has been or may be named explicitly and clearly; it is common in religious use and use with a series of closely related units.
Genre refers to a specific, named type; its use is mainly restricted to literature and art.