Remake

A remake is a (usually) completely new version of an older game that retells the story of the old game, with more modern methods and graphics or new additions in terms of gameplay mechanics or areas to explore. Not to be confused with a port.

Examples of Remakes

 * Metal Gear Solid: The Twin Snakes
 * Resident Evil (Remake)
 * Metroid: Zero Mission
 * Conker: Live and Reloaded

The game Doom 3 could be considered a remake of the first Doom game, since the plot and story are pretty much the same.