The Collaborative International Dictionary of English v.0.48:

Greek \Greek\, a. [AS. grec, L. Graecus, Gr. ?: cf. F. grec. Cf.
   Grecian.]
   Of or pertaining to Greece or the Greeks; Grecian.
   [1913 Webster]

   Greek calends. See under Greek calends in the vocabulary.


   Greek Church (Eccl. Hist.), the Eastern Church; that part
      of Christendom which separated from the Roman or Western
      Church in the ninth century. It comprises the great bulk
      of the Christian population of Russia (of which this is
      the established church), Greece, Moldavia, and Wallachia.
      The Greek Church is governed by patriarchs and is called
      also the Byzantine Church.

   Greek cross. See Illust. (10) Of Cross.

   Greek Empire. See Byzantine Empire.

   Greek fire, a combustible composition which burns under
      water, the constituents of which are supposed to be
      asphalt, with niter and sulphur. --Ure.

   Greek rose, the flower campion.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Byzantine \By*zan"tine\ (b[i^]*z[a^]n"t[i^]n), a.
   Of or pertaining to Byzantium. -- n. A native or inhabitant
   of Byzantium, now Constantinople; sometimes, applied to an
   inhabitant of the modern city of Constantinople. [Written
   also Bizantine.]
   [1913 Webster]

   Byzantine church, the Eastern or Greek church, as
      distinguished from the Western or Roman or Latin church.
      See under Greek.

   Byzantine empire, the Eastern Roman or Greek empire from a.
      d. 364 or a. d. 395 to the capture of Constantinople by
      the Turks, a. d. 1453.

   Byzantine historians, historians and writers (Zonaras,
      Procopius, etc.) who lived in the Byzantine empire. --P.
      Cyc.

   Byzantine style (Arch.), a style of architecture developed
      in the Byzantine empire.

   Note: Its leading forms are the round arch, the dome, the
         pillar, the circle, and the cross. The capitals of the
         pillars are of endless variety, and full of invention.
         The mosque of St. Sophia, Constantinople, and the
         church of St. Mark, Venice, are prominent examples of
         Byzantine architecture.
         [1913 Webster]

WordNet (r) 3.0 (2006):

Byzantine Church
    n 1: the Catholic Church as it existed in the Byzantine Empire
         [syn: Eastern Church, Byzantine Church]