Here are some Carnaby's Cockatoos I was able to photograph this morning

Well, I really can not tell the difference between Carnaby's and Baudin's. They are very similar, the only difference is the Baudin's have a slightly longer beak than Carnaby's.
The two breeds would need to be side by side for comparison.
There are up to 40,000 Carnaby's left in the wild.
There are less than 15,000 Baudin's left in the wild.
I see more Red Tailed Black Cockatoos in my area. Though there are definitely less than 10,000 of these left in the wild
Female Red Tailed Black Cockatoo
Male Red Tailed Black Cockatoo