Generally, macaws are the largest parrots. Image 3 Scarlet Macaw, note the long tail. Image 4 Cockatoos are usually a shade of white with added colors on the wings, tail and crest depending on the species. Their crest may be up or down depending on behavior. They have short tails.
Umbrella cockatoos are solid white.
This is a Sulfur Crested Cockatoo. Most cockatoos are from Australia. Image 5 Cockatiels are also from Australia and are much smaller birds with a crest and a long tail. They are the most common bird seen in pet bird practice and now come in a variety of genetically created colors. The hybrids are usually medically inferior to the common gray cockatiel seen here.