There are two species of Sulphur-crested Cockatoo, the Greater Sulphur-crested, often called just the Sulphur-crested, and the Lesser Sulphur-crested (lower down page), also called the Yellow-crested. The latter is smaller and has stronger yellow cheek patches. Both have several subspecies with slightly different appearance.
The Sulphur-crested Cockatoo comes mainly from Australia. The nominate subspecies may have a slight yellow blush to the cheek and has a very pale blue or white eye-ring.
Male and female have similar plumage. They are common in urban and rural eastern Australia (the two above in a Sydney park).
Shown above is the Triton subspecies, Cacatua galerita triton, which comes from New Guinea and adjacent islands. It has a stronger pale blue eye-ring.
The nominate Australian Sulphur-crested is larger, some 55 cm length. The Triton is some 45 cm length, as is the Medium Sulphur-crested subspecies (C. g. eleonora).
Triton Cockatoo with pale blue eye-ring.
With pale lemon crest raised.
The pale yellow under-wing.
Medium Sulphur-crested subspecies (C. g. eleonora), above, also called Eleonora Sulphur-crested Cockatoo.
The Yellow-crested Cockatoo confusingly has the scientific name Cacatua sulphurea, although it is also called the Lesser Sulphur-crested Cockatoo.
It is smaller than the Sulphur-crested at 35 cm length and has a slightly darker yellow crest and yellow patches on its white cheeks.
The Yellow-crested Cockatoo comes from Indonesia and East Timor. Male and female have similar plumage.
The smallest of the Yellow-crested subspecies, the critically-endangered Orange-crested Cockatoo is native to Sumba Island and the lesser Sunda Islands, Indonesia.