The Collaborative International Dictionary of English v.0.48:

Tuna \Tu"na\, n. [Cf. Tunny.]
   1. (Zool.) Any one of several species of large oceanic fishes
      belonging to the mackerel family Scombridae, especially
      the bluefin tuna (Thunnus thynnus, formerly Orcynus
      thynnus or Albacora thynnus), called also the common
      tunny or great tunny, a native of the Mediterranean Sea
      and of temperate parts of the Atlantic Ocean. It sometimes
      weighs a thousand pounds or more, and is caught
      commercially in large quantity for use as food; -- also
      called, especially in Britain, tunny. It is also one of
      the favorite fishes used by the Japanese in preparing
      sushi. On the American coast, especially in New England,
      it is sometimes called the horse mackerel. Another
      well-known species is the yellowfin tuna (Thunnus
      albacares) of warm seas. the See Illust. of Horse
      mackerel, under Horse.

   Note: The little tunny (Gymnosarda alletterata) of the
         Mediterranean and North Atlantic, and the long-finned
         tunny, or albacore (Thunnus alalunga) (see
         Albacore), are related species of smaller size.
         [1913 Webster +PJC]

   2. The bonito, 2.
      [1913 Webster]

   3. the meat of the tuna, used as food; -- also called tuna
      fish.
      [PJC]

The Collaborative International Dictionary of English v.0.48:

Tunny \Tun"ny\ (t[u^]n"n[y^]), n.; pl. Tunnies. [L. thunnus,
   thynnus, Gr. qy`nnos, qy^nos: cf. It. tonno, F. & Pr. thon.]
   (Zool.)
   The chiefly British equivalent of tuna; any one of several
   species of large oceanic fishes belonging to the Mackerel
   family, especially the common or great tunny (Thunnus
   thynnus syn. Albacora thynnus, formerly Orcynus thynnus)
   native of the Mediterranean Sea and the Atlantic Ocean. It
   sometimes weighs a thousand pounds or more, and is
   extensively caught in the Mediterranean. On the American
   coast it is called horse mackerel. See Illust. of Horse
   mackerel, under Horse. [Written also thynny.]
   [1913 Webster]

   Note: The little tunny (Gymnosarda alletterata) of the
         Mediterranean and North Atlantic, and the long-finned
         tunny, or albicore (Thunnus alalunga, see
         Albacore), are related species of smaller size.
         [1913 Webster]

WordNet (r) 3.0 (2006):

tunny
    n 1: important warm-water fatty fish of the genus Thunnus of the
         family Scombridae; usually served as steaks [syn: tuna,
         tuna fish, tunny]
    2: any very large marine food and game fish of the genus
       Thunnus; related to mackerel; chiefly of warm waters [syn:
       tuna, tunny]