Ah, so like with cockatiels - grey, cinnamon, lutino, etc?
I had always thought of things like that as different colorations, not so much as I guess breeding a “mixed breed” (using dog terminology).
Well, dog breeds are over hundreds or thousands of years... Their color, coat, temperament, etc, all taken into account.
Many bird species have been in captivity and bred with any purpose less than a hundred years. Some may only be a few generations away from the wild.
So take a wolf, the dog's ancestor. If you breed out different color mutations, like black, white, brown, grey, you have the same thing we are doing with cockatiels and conures. It's mostly surface level changes that can be done within a generation or two.
To breed so that you know your litter will be full of fierce, loyal hunters, or domestic wolves you can trust around your kids or sheep, that's going to take a lot longer.
We took wolves and made them into beings to fit our unique ways of life, styles of fighting or hunting.
For parrots we are still stuck on color. We haven't bred for traits yet. And it will take decades or centuries to do that.