A taxon (plural taxa) is any taxonomic unit. For example, the class Mammalia is a taxon which includes all mammalian species. Similarly, a species is a taxon, Panthera tigris being the tiger. This taxon contains lower taxa, which are sub-species, such as Panthera tigris tigris (Bengal tiger) or Panthera tigris sumatrae (Sumatran tiger).
Rank is simply the level of a taxon in the taxonomic heirarchy. For example, the taxa Mammalia and Aves both have the same rank since they are both classes. Panthera tigris sumatrae is of a lower rank than Panthera tigris because the former is a sub-species and the latter a species. Use of the term rank is only truly meaningful when comparing two taxa.
Taxonomic category is usually – for better or worse – used interchangeably with the term taxonomic rank. A Dictionary of Biology (6 ed.) certainly indicates that the terms rank and category are equivalent. The major taxonomic categories are domain, kingdom, phylum, class, order, family, genus, and species. A category can contain one or more taxa.
Another example, to summarize:
- Carnivora is a taxon, which contains many species including Vulpes
vulpes (red fox)
- Carnivora is in the category of order
- Carnivora (order) is a higher rank than Vulpes vulpes (species)