The Collaborative International Dictionary of English v.0.48:

Deer \Deer\ (d[=e]r), n. sing. & pl. [OE. der, deor, animal,
   wild animal, AS. de['o]r; akin to D. dier, OFries. diar, G.
   thier, tier, Icel. d[=y]r, Dan. dyr, Sw. djur, Goth. dius; of
   unknown origin. [root]71.]
   1. Any animal; especially, a wild animal. [Obs.] --Chaucer.
      [1913 Webster]

            Mice and rats, and such small deer.   --Shak.
      [1913 Webster]

            The camel, that great deer.           --Lindisfarne
                                                  MS.
      [1913 Webster]

   2. (Zool.) A ruminant of the genus Cervus, of many species,
      and of related genera of the family Cervid[ae]. The
      males, and in some species the females, have solid
      antlers, often much branched, which are shed annually.
      Their flesh, for which they are hunted, is called
      venison.
      [1913 Webster]

   Note: The deer hunted in England is Cervus elaphus, called
         also stag or red deer; the fallow deer is Cervus
         dama; the common American deer is Cervus
         Virginianus; the blacktailed deer of Western North
         America is Cervus Columbianus; and the mule deer of
         the same region is Cervus macrotis. See Axis,
         Fallow deer, Mule deer, Reindeer.
         [1913 Webster]

   Note: Deer is much used adjectively, or as the first part of
         a compound; as, deerkiller, deerslayer, deerslaying,
         deer hunting, deer stealing, deerlike, etc.
         [1913 Webster]

   Deer mouse (Zool.), the white-footed mouse (Peromyscus
      leucopus, formerly Hesperomys leucopus) of America.

   Small deer, petty game, not worth pursuing; -- used
      metaphorically. (See citation from Shakespeare under the
      first definition, above.) "Minor critics . . . can find
      leisure for the chase of such small deer." --G. P. Marsh.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Fallow deer \Fal"low deer`\ [So called from its fallow or pale
   yellow color.] (Zool.)
   A European species of deer (Cervus dama), much smaller than
   the red deer. In summer both sexes are spotted with white. It
   is common in England, where it is often domesticated in the
   parks.
   [1913 Webster]