The Collaborative International Dictionary of English v.0.48:

Capsicum \Cap"si*cum\ (k[a^]p"s[i^]*k[u^]m), n. [NL., fr. L.
   capsa box, chest.] (Bot.)
   A genus of plants of many species, producing capsules or dry
   berries of various forms, which have an exceedingly pungent,
   biting taste, and when ground form the red or Cayenne pepper
   of commerce.
   [1913 Webster]

   Note: The most important species are Capsicum baccatum or
         bird pepper, Capsicum fastigiatum or chili pepper,
         Capsicum frutescens or spur pepper (from which
         tabasco is obtained), Capsicum chinense, which
         includes the fiery-hot habanero pepper, and Capsicum
         annuum or Guinea pepper, which includes the bell
         pepper, the jalapeno pepper, the cayenne pepper, and
         other common garden varieties. The fruit is much used,
         both in its green and ripe state, in pickles and in
         cookery. 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 Cayenne pepper,
         pepper and http://www.chili-pepper-plants.com/.
         [1913 Webster + PJC]

   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); .
      [1913 Webster + PJC]

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):

Capsicum frutescens
    n 1: plant bearing very hot medium-sized oblong red peppers;
         grown principally in the Gulf Coast states for production
         of hot sauce [syn: tabasco pepper, hot pepper, tabasco
         plant, Capsicum frutescens]