The male’s red cap is a full one, worn pulled down to his beak, while the female has a smaller, almost beany-like, cap worn at the back of her head. (The male also has red-feathered war paint streaming back from his beak, making him look fearsome.) The cap is the characterizing feature of the birds and the reason it has a Latinized name.
“Pileated” is derived from the Latin words for conical felt caps. Thus, this bird is a capped or crested bird. (By the way, the similar word “pileum” is the name for the area on any bird from the top of its head to its nape.) There is a debate, however, as to how to pronounce “pileated.”
The world seems to be divided between pie- eaters and pill-takers when it comes to pileated. That is, some say “PIE-lee-Ay-tid” and some say “PILL-ee-Ay-tid.” Both pronunciations seem to be well-accepted by birders, but English teachers will say that the pie people are technically correct. (Images taken in Brooklin, Maine, on September 25, 2023.)