His countryman Anton Reichenow classified Purpureicephalus as a subgenus of Platycercus before placing it in the genus Porphyreicephalus (later corrected to Porphyrocephalus), until 1912, when Australian amateur ornithologist Gregory Mathews re-established the genus as Purpureicephalus. The red-capped parrot's elongated bill and its unusual coloration—lack of cheek patches compared with Platycercus—are the main reasons for its placement in its own genus. No subspecies are recognised currently. Mathews tentatively described a subspecies carteri in 1915 from a specimen collected at Broomehill on the basis of darker upperparts and greener cheeks; it was not considered distinct by later authors. There is no known geographical variation; five birds from Esperance had smaller bills and tarsi than individuals from elsewhere in its range, but the sample was too small to draw any conclusions. The red-capped parrot is related to other broad-tailed parrots, but relationships within the group had been unclear. In 1938, Australian ornithologist Dominic Serventy proposed that it was the sole survivor of a lineage of eastern Australian origin, with no close living relatives. In 1955, British evolutionary biologist Arthur Cain proposed that the eastern lineage had vanished after being outcompeted by the crimson rosella (Platycercus elegans), and that its closest relative was the horned parakeet (Eunymphicus cornutus) of New Caledonia, which he concluded had adopted a much greener plumage of a wetter climate. A 2011 genetic study including nuclear and mitochondrial DNA found that the red-capped parrot was closely related to the mulga parrot (Psephotellus varius), the two lineages having diverged in the Miocene. The combined lineage itself diverging from one giving rise to the hooded parrot (Psephotellus dissimilis) and golden-shouldered parrot (Psephotellus chrysopterygius). "Red-capped parrot" has been designated the official name by the International Ornithologists' Union (IOC). English ornithologist John Gould used the name "red-capped parakeet" in 1848 based on Vigors' scientific name, which also inspired the old avicultural term "pileated parrot". It has also been called "western king parrot" to distinguish it from the Australian king parrot (Alisterus scapularis) occurring in the east, "purple-crowned parrot", "grey parrot", or "hookbill" for the distinctive upper mandible. The name "pileated parakeet" potentially causes confusion among aviarists with the South American pileated parrot (Pionopsitta pileata). Gould also reported "blue parrot" as an early colonial name. The name "king parrot" has persisted in Western Australia, English naturalist W. B. Alexander commenting that it was always known by this name in a field note in 1917, Pizzey