The Collaborative International Dictionary of English v.0.48:

Paroquet \Par"o*quet`\, n. [F. perroquet, or Sp. periquito; both
   prob. orig. meaning, little Peter. See Parrot.] (Zool.)
   Same as Parrakeet. [Written also paroket, parroquet,
   and perroquet.]
   [1913 Webster]

   Paroquet auk or Paroquet auklet (Zool.), a small auk
      (Cyclorrhynchus psittaculus) inhabiting the coast and
      islands of Alaska. The upper parts are dark slate, under
      parts white, bill orange red. Called also perroquet auk.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Parrakeet \Par"ra*keet`\ (p[a^]r"r[.a]*k[=e]t`), Parakeet
\Par"a*keet`\, n. [See Paroquet.] (Zool.)
   Any one of numerous species of small parrots having a
   graduated tail, which is frequently very long; -- called also
   paroquet and paraquet.
   [1913 Webster]

   Note: Many of the Asiatic and Australian species belong to
         the genus Paleornis; others belong to Polytelis,
         Platycercus, Psephotus, Euphema, and allied
         genera. The American parrakeets mostly belong to the
         genus Conurus, as the Carolina parrakeet (Conurus
         Carolinensis).
         [1913 Webster] Parral

WordNet (r) 3.0 (2006):

paroquet
    n 1: any of numerous small slender long-tailed parrots [syn:
         parakeet, parrakeet, parroket, paraquet,
         paroquet, parroquet]