The Collaborative International Dictionary of English v.0.48:

Pepper \Pep"per\ (p[e^]p"p[~e]r), n. [OE. peper, AS. pipor, L.
   piper, fr. Gr. pe`peri, pi`peri, akin to Skr. pippala,
   pippali.]
   1. A well-known, pungently aromatic condiment, the dried
      berry, either whole or powdered, of the Piper nigrum.
      [1913 Webster]

   Note: Common pepper, or black pepper, is made from the
         whole berry, dried just before maturity; white pepper
         is made from the ripe berry after the outer skin has
         been removed by maceration and friction. It has less of
         the peculiar properties of the plant than the black
         pepper. Pepper is used in medicine as a carminative
         stimulant.
         [1913 Webster]

   2. (Bot.) The plant which yields pepper, an East Indian woody
      climber (Piper nigrum), with ovate leaves and apetalous
      flowers in spikes opposite the leaves. The berries are red
      when ripe. Also, by extension, any one of the several
      hundred species of the genus Piper, widely dispersed
      throughout the tropical and subtropical regions of the
      earth.
      [1913 Webster]

   3. Any plant of the genus Capsicum (of the Solanaceae
      family, which are unrelated to Piper), and its fruit;
      red pepper; chili pepper; as, the bell pepper and the
      jalapeno pepper (both Capsicum annuum) and the
      habanero pepper (Capsicum chinense); . These contain
      varying levels of the substance capsaicin (C18H27O3N),
      which gives the peppers their hot taste. The habanero is
      about 25-50 times hotter than the jalapeno according to a
      scale developed by Wilbur Scoville in 1912. See also
      Capsicum and http://www.chili-pepper-plants.com/.
      [1913 Webster + PJC]

   Note: The term pepper has been extended to various other
         fruits and plants, more or less closely resembling the
         true pepper, esp. to the common varieties of
         Capsicum. See Capsicum, and the Phrases, below.
         [1913 Webster]

   African pepper, the Guinea pepper. See under Guinea.

   Cayenne pepper. See under Cayenne.

   Chinese pepper, the spicy berries of the Xanthoxylum
      piperitum, a species of prickly ash found in China and
      Japan.

   Guinea pepper. See under Guinea, and Capsicum.

   Jamaica pepper. See Allspice.

   Long pepper.
      (a) The spike of berries of Piper longum, an East Indian
          shrub.
      (b) The root of Piper methysticum (syn. Macropiper
          methysticum) of the family Piperaceae. See Kava.


   Malaguetta pepper, or Meleguetta pepper, the aromatic
      seeds of the Amomum Melegueta, an African plant of the
      Ginger family. They are sometimes used to flavor beer,
      etc., under the name of grains of Paradise.

   Red pepper. See Capsicum.

   Sweet pepper bush (Bot.), an American shrub (Clethra
      alnifolia), with racemes of fragrant white flowers; --
      called also white alder.

   Pepper box or Pepper caster, a small box or bottle, with
      a perforated lid, used for sprinkling ground pepper on
      food, etc.

   Pepper corn. See in the Vocabulary.

   Pepper elder (Bot.), a West Indian name of several plants
      of the Pepper family, species of Piper and Peperomia.


   Pepper moth (Zool.), a European moth (Biston betularia)
      having white wings covered with small black specks.

   Pepper pot, a mucilaginous soup or stew of vegetables and
      cassareep, much esteemed in the West Indies.

   Pepper root. (Bot.). See Coralwort.

   pepper sauce, a condiment for the table, made of small red
      peppers steeped in vinegar.

   Pepper tree (Bot.), an aromatic tree (Drimys axillaris)
      of the Magnolia family, common in New Zealand. See
      Peruvian mastic tree, under Mastic.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Cayenne \Cay*enne\, n. [From Cayenne, a town and island in
   French Guiana, South America.]
   Cayenne pepper.
   [1913 Webster]

   Cayenne pepper.
   (a) (Bot.) A species of Capsicum (Capsicum frutescens)
       with small and intensely pungent fruit.
   (b) A very pungent spice made by drying and grinding the
       fruits or seeds of several species of the genus
       Capsicum, esp. Capsicum annuum and Capsicum
       Frutescens; -- called also red pepper. It is used
       chiefly as a condiment.
       [1913 Webster]

WordNet (r) 3.0 (2006):

red pepper
    n 1: ground pods and seeds of pungent red peppers of the genus
         Capsicum [syn: cayenne, cayenne pepper, red pepper]
    2: very hot red peppers; usually long and thin; some very small
       [syn: tabasco, red pepper]