What are the types of greater sulphur cresteds?

Greaters are Galerita Galeritas. Med are Eleanoras, and Tritons. Then theres the lesser. I think Citron falls somewhere in between.

The Galerita is a big bird. Very sweet but demanding of attention. Packs a wicked bite.

This is a very good informational article;

The Sulphur Crested Cockatoos
by Sandra Dobbs and Carol Highfill

BirdsnWays Cockatoo Heaven - Sulphur Crested Species

What is the difference between a triton and a galerita?

Triton is a little smaller, and the crest is a different with more of an orange color.

Does anybody on this board own a galerita?

Someone who doesnt frequent here anymore who lives in Australia had a rehome. She had to be rehome her again due to screaming issues and the neighbors being bothered. Are you considering one? PLEASE..carefully think this out. They are BIG NOISY BIRDS. When they love you its with all their might! But when they want their own way, you must be prepared to deal with it, its not easy. It takes a special person to deal with this demanding species.

I don't know, maybe some day; anything's possible. Nowhere in the near future though.
If I ever do decide to get one, I will think it through very carefully and do lots of research. These questions were mostly out of curiousity, though.
Thanks for your help Leigh!
Max