"Greatest Hits are video games for the American Sony PlayStation, PlayStation 2, PlayStation 3, and PlayStation Portable consoles that have been officially re-released at a lower price by Sony.
While Greatest Hits titles are usually just a reprinting of the original game with altered packaging and a lower price, occasionally a game is given a "special edition" of its original version, released under the Greatest Hits label. Usually these additions are small bonuses, such as the inclusion of new game demos or soundtrack CDs, or slight improvements such as adding analog control or vibration functionality to games that did not have these features in their original releases. Occasionally, significant changes are implemented into the game. Noteworthy examples of this are the Greatest Hits special editions of Devil May Cry 3: Dante's Awakening, Dragon Ball Z: Budokai 3, Midnight Club 3: DUB Edition Remix, Silent Hill 2 and Virtua Fighter 4: Evolution, which were enhanced significantly from their original releases with added characters, levels, modes, features, etc. However, "special edition" enhancements such as these are typically uncommon in Greatest Hits releases.
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Source: Wikipedia, "List_of_Sony_Greatest_Hits_games", available under the CC-BY-SA License.