The Collaborative International Dictionary of English v.0.48:

Walnut \Wal"nut\, n. [OE. walnot, AS. wealh-hnutu a Welsh or
   foreign nut, a walnut; wealh foreign, strange, n., a
   Welshman, Celt (akin to OHG. Walh, properly, a Celt, from the
   name of a Celtic tribe, in L. Volcae) + hnutu a nut; akin to
   D. walnoot, G. walnuss, Icel. valhnot, Sw. valn["o]t, Dan
   valn["o]d. See Nut, and cf. Welsh.] (Bot.)
   The fruit or nut of any tree of the genus Juglans; also,
   the tree, and its timber. The seven or eight known species
   are all natives of the north temperate zone.
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   Note: In some parts of America, especially in New England,
         the name walnut is given to several species of hickory
         (Carya), and their fruit.
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   Ash-leaved walnut, a tree (Juglans fraxinifolia), native
      in Transcaucasia.

   Black walnut, a North American tree (Juglans nigra)
      valuable for its purplish brown wood, which is extensively
      used in cabinetwork and for gunstocks. The nuts are
      thick-shelled, and nearly globular.

   English walnut, or European walnut, a tree (Juglans
      regia), native of Asia from the Caucasus to Japan,
      valuable for its timber and for its excellent nuts, which
      are also called Madeira nuts.

   Walnut brown, a deep warm brown color, like that of the
      heartwood of the black walnut.

   Walnut oil, oil extracted from walnut meats. It is used in
      cooking, making soap, etc.

   White walnut, a North American tree (Juglans cinerea),
      bearing long, oval, thick-shelled, oily nuts, commonly
      called butternuts. See Butternut.
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The Collaborative International Dictionary of English v.0.48:

Butternut \But"ter*nut`\, n.
   1. (Bot.) An American tree (Juglans cinerea) of the Walnut
      family, and its edible fruit; -- so called from the oil
      contained in the latter. Sometimes called oil nut and
      white walnut.
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   2. (Bot.) The nut of the Caryocar butyrosum and Caryocar
      nuciferum, of S. America; -- called also Souari nut.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Juglans cinerea
    n 1: North American walnut tree having light-brown wood and
         edible nuts; source of a light-brown dye [syn: butternut,
         butternut tree, white walnut, Juglans cinerea]