I know they came with different games, but do they differ in terms of lore? Does one get respecced so to speak? Also why is there no PGE 2nd edition?

PGE 1E is much more biased, with differing viewpoints and more interesting annotations and tidbits due to the Imperial Geographical Society's propaganda and uncertainty over several issues.

PGE 3E is much more third era focused, no annotations, and much more historical information about the lands and the environment. Not as much propaganda either, and centuries of living as one has lessened the uncertainty over each other.

The Emperor's Guide is a fusion of the First Edition and Third Edition.

There is no Second Edition because it was banned and destroyed (in popular community-headcanon anyways).

Fragments do exist.