The Collaborative International Dictionary of English v.0.48:

Prickly ash \Prickly ash\ (Bot.),
   1. A prickly shrub (Xanthoxylum Americanum) with yellowish
      flowers appearing with the leaves; also called toothache
      tree. All parts of the plant are pungent and aromatic.
      The southern species is Xanthoxylum Carolinianum.
      --Gray.
      [1913 Webster]

   2. (Bot.), Hercules'-club, also called the Angelica tree.
      [PJC]

The Collaborative International Dictionary of English v.0.48:

Hercules'-club \Hercules'-club\, Hercules'-club
\Hercules'-club\, Hercules-club \Hercules-club\prop. n.
   1. (Bot.) A densely spiny ornamental tree (Zanthoxylum
      clava-herculis) of the rue family, growing in southeast
      U. S. and West Indies. [WordNet sense 1]

   Note: It belongs to the same genus as one of the trees
         (Zanthoxylum Americanum) called prickly ash.

   Syn: Hercules'-clubs, Hercules-club, Zanthoxylum
        clava-herculis.
        [1913 Webster + WordNet 1.5]

   2. A small, prickly, deciduous clump-forming tree or shrub
      (Aralia spinosa) of eastern U.S.; also called Angelica
      tree and prickly ash. [WordNet sense 2]

   Syn: American angelica tree, devil's walking stick, Aralia
        spinosa.
        [1913 Webster + WordNet 1.5]

   3. A variety of the common gourd (Lagenaria vulgaris). Its
      fruit sometimes exceeds five feet in length.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Ash \Ash\ ([a^]sh), n. [OE. asch, esh, AS. [ae]sc; akin to OHG.
   asc, Sw. & Dan. ask, Icel. askr, D. esch, G. esche.]
   1. (Bot.) A genus of trees of the Olive family, having
      opposite pinnate leaves, many of the species furnishing
      valuable timber, as the European ash (Fraxinus
      excelsior) and the white ash (Fraxinus Americana).
      [1913 Webster]

   Prickly ash (Zanthoxylum Americanum) and Poison ash
      (Rhus venenata) are shrubs of different families,
      somewhat resembling the true ashes in their foliage.

   Mountain ash. See Roman tree, and under Mountain.
      [1913 Webster]

   2. The tough, elastic wood of the ash tree.
      [1913 Webster]

   Note: Ash is used adjectively, or as the first part of a
         compound term; as, ash bud, ash wood, ash tree, etc.
         [1913 Webster]

WordNet (r) 3.0 (2006):

prickly ash
    n 1: any of a number of trees or shrubs of the genus Zanthoxylum
         having spiny branches
    2: Australian tree having alternate simple leaves (when young
       they are pinnate with prickly toothed margins) and slender
       axillary spikes of white flowers [syn: prickly ash, Orites
       excelsa]