The Collaborative International Dictionary of English v.0.48:

Osier \O"sier\, n. [F. osier: cf. Prov. F. oisis, Armor. ozil,
   aozil, Gr. ?, ?, ?, L. vitex, and E. withy.] (Bot.)
      (a) A kind of willow (Salix viminalis) growing in wet
          places in Europe and Asia, and introduced into North
          America. It is considered the best of the willows for
          basket work. The name is sometimes given to any kind
          of willow.
      (b) One of the long, pliable twigs of this plant, or of
          other similar plants.
          [1913 Webster]

                The rank of osiers by the murmuring stream.
                                                  --Shak.
          [1913 Webster]

   Osier bed, or Osier holt, a place where willows are grown
      for basket making. [Eng.]

   Red osier.
      (a) A kind of willow with reddish twigs (Salix rubra).
      (b) An American shrub (Cornus stolonifera) which has
          slender red branches; -- also called osier cornel.
          [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Withy \With"y\, n.; pl. Withies. [OE. withe, wipi, AS.
   w[imac]?ig a willow, willow twig; akin to G. weide willow,
   OHG. w[imac]da, Icel. v[imac]?ja, a withy, Sw. vide a willow
   twig, Dan. vidie a willow, osier, Gr. ?, and probably to L.
   vitis a vine, viere to plait, Russ. vite. [root]141. Cf.
   Wine, Withe.]
   [1913 Webster]
   1. (Bot.) The osier willow (Salix viminalis). See Osier,
      n.
      (a) .
          [1913 Webster]

   2. A withe. See Withe, 1.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Salix viminalis
    n 1: willow with long flexible twigs used in basketry [syn:
         common osier, hemp willow, velvet osier, Salix
         viminalis]