Taxonomic and evolutionary species (T-species and E-species) can be viewed as distinct ontologically. Conventional taxonomic species are cognitive concepts, refined by biological theory, which tessellate the living world into comprehensible but imperfectly delimited units to provide an overview of biodiversity – the public domain status quo species system. A single named taxonomic species may consist of multiple species taxon concepts, each of which is objectified by the specimen sets used – Simpson's hypodigms. The resulting compound species taxon may thus be vague. Evolutionary species are predicted from evolutionary theory, and serve as models for investigating evolutionary processes. They are tools for biologists to probe deeper into biological reality and generate hypotheses of patterns that lie beyond the confines of human cognition. Cryptic species of result from the feedback to taxonomy of discoveries in evolutionary biology and may differ from species taxa in data, analysis method, or species criterion. Their recognition as taxonomic species requires social convention among biologists, especially systematists and they should be objectified as published taxon concepts using protocols including description, diagnosis, hypodigm and a correct name. The public domain taxon system would benefit if species taxon concepts werebased on a system of online databases