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]