Parakeets, conures and parrot are all general terms. A parrot is any parrot-type bird including conures and parakeets. A parakeet is any small, long-tailed parrot. Conures are a collection of small to medium sized South American parrots, relatively long-tailed, with a white-eye-ring.
See also: Alexandrine parakeet, Brown throated parakeet, Derbyan parakeet, Olive-throated Parakeet, Orange-chinned Parakeet, Orange fronted parakeet / conure, Painted conure, Patagonian conure, Plum headed parakeet, Red fronted conure, Red-masked Parakeet, Rose-ringed parakeet, Scarlet fronted parakeet, Sun conure