Both of these are on sale and it is the only thing that comes up if I search for Geneforge on GOG besides a hint book. Does Geneforge Saga contain Geneforge 1: Mutagen? Is Mutagen a remastered version of what comes in the Saga? How much of a remaster?

Geneforge Saga, as the title suggests, contains all the five games of the original series.
Geneforge 1 - Mutagen is the remake of the first game in the series. featuring an enhanced game engine, a redone interface, new areas, quests, characters and dialogue and some differences in the gameplay.
The other games of the series have not been remastered yet, but a Kickstarter campaign for the remake of Geneforge 2 is running right now and it has already been successfully funded.