(Greater) Sulphur-crested Cockatoo Cacatua galerita

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.
Sulphur-crested Cockatoo
Sulphur-crested Cockatoo
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).
Triton Sulphur-crested Cockatoo
Triton Cockatoo
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 - just like that
Sulfur-crested Cockatoo Triton Cockatoo with pale blue eye-ring.
Triton Cockatoo
Sulphur-crested Cockatoo Triton Cockatoo with crest raised.
Sulphur-crested Cockatoo Nominate Sulphur-crested Cockatoos in downtown Sydney.
Sulphur-crested Cockatoo Very pale yellow under-wing and under-tail.
Sulphur-crested Cockatoo
Sulphur-crested Cockatoo
With pale lemon crest raised.
Sulphur-crested Cockatoo
The pale yellow under-wing.
Medium Sulphur-crested Cockatoo
Eleonora Sulphur-crested Cockatoo
Eleonora Sulphur-crested Cockatoo
Medium Sulphur-crested subspecies (C. g. eleonora), above, also called Eleonora Sulphur-crested Cockatoo.

Lesser Sulphur-crested/ Yellow-crested Cockatoo Cacatua sulphurea

Sulphur-crested Cockatoo
Greater 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.
Lesser Sulphur-crested Cockatoo
Yellow-crested Cockatoo
The Yellow-crested Cockatoo comes from Indonesia and East Timor. Male and female have similar plumage.
Lesser Sulfur-crested Cockatoo
Sulphur-crested Cockatoo
Sulphur-crested Cockatoo
This is the nominate subspecies.
Lesser Sulfur-crested Cockatoo
Sulphur-crested Cockatoo
Sulphur-crested Cockatoo
The "Two-horned Goat Cockatoo"!
Orange-crested Cockatoo
Orange-crested Cockatoo
Citron-crested Cockatoo
One of the other subspecies (shown above/below) is called the Citron-crested (Cacatua sulphurea citrinocristata) but actually has an orange crest. It is also known as the Orange-crested.
Orange-crested Cockatoo
Orange-crested Cockatoo
Citron-crested Cockatoo
The smallest of the Yellow-crested subspecies, the critically-endangered Orange-crested Cockatoo is native to Sumba Island and the lesser Sunda Islands, Indonesia.
Orange-crested Cockatoo with chip on shoulder
Orange-crested Cockatoo
Citron-crested Cockatoo with chip on shoulder
"I've got a chip on my shoulder. -- Well, let's not understate it -- I've got a great big chip on my shoulder."