In the original Hyperdimension Neptunia, the Super Dimension consisted of two worlds: Celestia and Gamindustri. Originally, Gamindustri was ruled by only one goddess, Arfoire. However, Arfoire lost control of herself and nearly destroyed the world. Due to the efforts of the four legendary heroes from Planeptune, Lastation, Lowee, and Leanbox, the world was saved. Arfoire promised to never abuse her powers ever again and separated a part of her power from herself. This was the birth of Histoire, the tome responsible for recording every event in history and essentially the world itself.
After this event, Arfoire had no longer wished to rule the world by herself and decided created four new CPUs: Neptune, Noire, Blanc, and Vert. These four goddesses contained only a quarter of the power of a true goddess. Each of them were responsible for one of the four nations in Gamindustri.
In this Gamindustri, each nation was it's own landmass and movement between the nations was done via Terraportation. In order for Terraportation to be done, two landmass would need to be in incoming range of each other to pass through to the other side.
The Guild was known as a group of so-called Heretics. Not all of them serve directly under the Basilicom, but they each worship a different goddess than the one on their native land. It's creation was due to the purge against on Leanbox which lead most to flee to Lowee. Due to this, Lowee created a city for The Guild called "Guild City."
Hyperdimension Neptunia Re;Birth1
While the geographical structure and means of transportation remain unchanged, the world's history has. The Guild functions the same as it would in the Hyperdimension and serves under the Basilicom. The original goddess and Arfoire are now two different beings, with the latter a human who used her power of copying to aid the legendary heroes.