Lori, to get a good understanding of the answer to your question, you need to have a basic understanding of the scientific classification of all life on the planet, but as a short answer, our feathered friends were classified, primarily by the shape of their beaks, them by the similarities one specie may have to another, then by where they live & how they might be related to another similar specie, looking for a separate or subspecies.....
Some of the key words you might want to learn and/or learn about are:
KINGDOM – “Animalia” (animal). The “kingdom” includes all living organisms: animal, plant, fungi, bacteria (single-celled organisms without a nucleus) and protists (single-celled organisms with a nucleus).
PHYLUM – “Chordata“. Phylum furthers categorizes the ranking of those in the animal kingdom. The group “chordata” includes all vertabrate animals (those with spinal chords). In the animal kingdom there are 36 animal phyla.
CLASS – “Aves“. The aves group includes only birds and indicates that its members have feathers.
ORDER – “Psittaciformes“. Refers specifically to parrots.
FAMILY – “Cacatuidae“. This group includes ALL cockatoos – including the cockatiel.
SUB FAMILY – “Cacatuinae”. This category refers specifically to the white cockatoos.
GENUS – “Cacatua“. The genus refers to a group of birds that have certain defining characteristics in common.
SPECIES – “goffini“. Finally we arrive at the one and only goffins cockatoo – totally unique unto itself. In order to point to the exact classification of this species, you need only two words: cacatua goffini – its “scientific name”.
SUBSPECIES – none. Some parrots, the lesser sulphur crested cockatoos, for instance, evolve ever so slightly differently. They may fall into all of the same above categories, but one may be slightly larger or have pale cheek patches that make it still more unique. They would be further classified by way of subspecies.
Here are several links you might be interested in:
The Taxonomy and Classification of Parrots | Peggy's Parrot Place
ADW: Psittacidae: CLASSIFICATION
Parrot - Wikipedia, the free encyclopedia
Bird Classifications - Birds.com: Online Birds Guide with Facts, Articles, Videos, and Photos
Hope that helps answer your question.....