The toucans belong to the order Piciformes.

The relatives of the toucan are other piciformes, such as woodpeckers and barbets.

Picariae Woodpecker Order: Piciformes Family: Picidae

No a toucan is not a parrot. Toucans, or ramphastids are a family of birds in the order piciformes. Woodpeckers, and barbets are also in the order piciformes. Parrot actually refers to an entire order of birds, the psitticiformes, and since toucans are piciformes rather than psitticiformes they are not a parrot.

If you are referring to birds, the general scientific name for them is Aves. Their higher classification is Tetrapod. Some lower classifications are: Charadriiformes, Piciformes, Owl, or Bucerotiformes.