This species was first described as
Cardinalis sinuatus by Bonaparte in 1838 and
Pyrrhuloxia was introduced as a genus name by the same Bonaparte in 1850 (here:
Conspectus generum Avium) to include this single species (monospecific genus); the genus was described based on the shape of the bill, and from the OD (in Latin) we take that Pyrrhuloxia derivates from Pyrrhos (fire red, from the Greek: Πύρρος) and loxia (the next species included by the author was Loxia cardinalis, the Red Cardinal); the bill is not compared to that of Pyrrhula, but to that of the Parrotbills (Parodoxornis, an Asian genus, and that precedes Pyrrhuloxia in the same work) in having a sinuous cutting edge and very curved culmen (thus being "almost intermediate between Paradoxornis and the Red Cardinal").
So we have two candidate etymologies, then ?
Although it is true that the bird is nowhere directly compared to
Pyrrhula, I don't really see anything in the original texts, either, suggesting that
πυρρός ("fire red") played a direct role in the creation of this name. [
πυρρός + loxia] would not account for the
u in
Pyrrhuloxia.
In the
Conspectus, the subgenus
Pyrrhuloxia is described as "
Rubro colore tantum indutus !", which means something like "Only adorned with red colour !", and is obviously intended to have a counterpart in "
Color (maris)
ruberrimus !" ("Colour (of male) extremely red !"), which characterises subgenus
Cardinalis. I.e., if anything,
Pyrrhuloxia would seem to be described as not-very-red in comparison to its putative closest relative.
Incidentally, I would tend to take this name from Bonaparte & Schlegel's
Monographie des Loxiens (
https://www.biodiversitylibrary.org/page/33463784 ; either 11 Nov 1850, or 9 Dec 1850, depending on whether one accepts [
this] as conclusive evidence, or just [
that]), not from the
Conspectus (I known no evidence that allows dating this part to earlier than 31 Dec 1850; early 1851 is far from excluded, actually).
Two candidate ODs as well, thus.
