Though only represented by two small, jointed and vaguely cylindrical fossil fragments (both discovered in the Portage sandstones of Italy, New York), the species today recognised as H. wrightianus has had a complicated taxonomic history. Originally described in 1881 as a species of plant, the fragmentary fossil referred to as "Equisetides wrightiana" was noted to represent the fossil remains of a eurypterid by American paleontologist James Hall in 1884, three years later. Though Hall assigned the species to Stylonurus, that same year British paleontologists Henry Woodward and Thomas Rupert Jones assigned the fossil to the genus Echinocaris, believing the fossils represented a phyllocarid crustacean. The assignment to Echinocaris was probably based on the slightly spinose surface of the fossils, but in 1888 Hall and American paleontologist John Mason Clarke pointed out that no described Echinocaris actually had spines similar to what Woodward and Jones suggested and as such, reassigned the species back to Stylonurus, interpreting the fossils as fragments of the long walking legs. An assignment to Stylonurus was affirmed by Clarke and American paleontologist Rudolf Ruedemann in their influential The Eurypterida of New York in 1912, though no distinguishing features of the fossils were given due to their fragmentary nature.
