There are over 40 different types of cockatoo.
In captivity one most often sees the pinkish moluccan cockatoo, the white umbrella cockatoo or the sulphur crested cockatoo. The last-mentioned comes in three different sizes: Lesser, Mediumand Greater - these are all separate species but share in common a pronounced yellow crest and a delicate yellow blush to the white of the underside of the wings.
Cockatoos are strong flyers (the smaller ones can almost hover) and need plenty of exercise and supervised freedom, a large outside, stimulating play aviary for days of good weather. Cockatoos are highly intelligent, emotional, sensitive birds and will easily suffer neurotic behaviour, leading to self-mutilation under captive conditions. Their highly-strung nature makes themeasily susceptible to suffering claustrophobia when confined to cages for long periods. Males are highly aggressive during peak hormonal breeding periods.
Behaviourally they are perhaps the most difficult of all parrot to keep in the home and therefore should not be considered or termed as a pet to keep in the home. One should especially never keep a single pet cockatoo alone at home all day while out at work. Cockatoos are noisier than macaws - the larger cockatoos have a vocal range of one mile or more and are especially noisy when they want something (usually ones attention).
Cockatoos are very good at escaping from their cages and can even open locked padlocks (think about it!). Once out in the house, nothing is safe from a cockatoo's urge to chew things up. If you are going to get angry about this, don't get a cockatoo because it will happen!
The biggest cockatoo is the Palm cockatoo (60 cm). They are thankfully rare in captivity. An unusual feature is a patch of skin on the face, the colour of which the bird can change to signal its emotional state.
Umbrella cockatoos (also called the Greater White Crested) are just a tad smaller than moluccans and are white with a lemon yellow blush under their wings and tail. They are similar in personality to moluccans (this also means they are just as demanding and subject to the same emotional problems if you leave them alone all day). These parrots have a large white crest used for signalling and communication with you and its fellows. Pet umbrellas like to be cuddled and cossetted for hours, so do not buy one if you cannot provide this.
Leadbeater's cockatoos (also called Major Mitchell) are about 45 cm long and have wonderful pink and white feathers on the body with a striped yellow and red crest, the ends of the feathers of which are tipped with white!
The smallest cockatoo is the Goffin (about 25 cm) followed by the Timor cockatoo (30 cm).
The Galah (also called the rose-breasted) is one of the gaudiest cockatoos: they have pink breast feathers with grey feathers on the wing and back. The crest is white and pink. Pretty they may be but in Australia where they come from, farmers regard them as vermin because huge flocks come down to the fields and destroy everything. Thousands are culled inhumanely every year by farmers.