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The term "old world" is used in the World of Warcraft community to denote the parts of the in-game Azeroth that have existed since vanilla WoW, before the expansions. As commonly understood, the old world does not include the Azuremyst Isles and Quel'Thalas (which were added to Kalimdor and the Eastern Kingdoms, respectively, in The Burning Crusade), nor Outland and Northrend.
This term was also used internally by the developers, as seen by the filename oldworld.mpq in patch 4.0.1 and patch 4.0.3, which contains the classic versions of Kalimdor and the Eastern Kingdoms — as opposed to world.mpq, containing the versions introduced with the world update in patch 4.0.3a.
It remains to be seen whether these continents will continue to be called "the old world" now that the Shattering has taken place and brought a major redesign of terrain and questing experience.