Linnaean taxonomy is either
- the particular classification (taxonomy) of Linnaeus, as set forth in his Systema Naturae (1735) and subsequent works. In the taxonomy of Linnaeus there are three kingdoms, divided into classes, and they, in turn, into orders, genera (singular: genus), and species (singular: species), with an additional rank lower than species.
- a term for rank-based classification of organisms, in general. That is, taxonomy in the traditional sense of the word: rank-based scientific classification, This term is especially used as opposed to cladistic systematics, which groups organisms into clades. It is attributed to Linnaeus, although he neither invented the concept (it goes back to Aristotle) nor gave it its present form. In fact, it does not have an exact present form, Linnaean taxonomy is a collective term for what actually are several separate fields, which use similar approaches.
The same applies to "Linnaean name": depending on context this may either be a formal name given by Linnaeus (personallly), such as Giraffa camelopardalis Linnaeus, 1758, or a formal name in the accepted nomenclature (as opposed to a modernistic clade name).