Glossy Black Cockatoo
Calyptorhynchus lathami
Like the related red-tailed black cockatoo, this species is sexually dimorphic. The male glossy black cockatoo is predominantly black with a chocolate-brown head and striking caudal red patches. The female is a duller dark brown, with flecks of yellow in the tail and collar. The female's tail is barred whereas the male's tail is patched. An adult will grow to be about 46–50 cm (18–19.5 in) in length.
ID text from Wikipedia, CC BY-SA 4.0

Red-tailed Black Cockatoo
Calyptorhynchus banksii
Red-tailed black cockatoos are around 60 centimetres (24 in) in length and sexually dimorphic. The male's plumage is all black with a prominent black crest made up of elongated feathers from the forehead and crown. The bill is dark grey. The tail is also black with two lateral bright red panels. Females are black with yellow-orange stripes in the tail and chest, and yellow grading to red spots on the cheeks and wings. The bill is pale and horn-coloured. The underparts are barred with fine yellow over a black base. Male birds weigh between 670 and 920 grams (1.48 and 2.
ID text from Wikipedia, CC BY-SA 4.0
Where you might meet both
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Play today's Daily BirdPhotos and recordings are credited to their authors under the licence shown. Full profiles: Glossy Black Cockatoo and Red-tailed Black Cockatoo.