How do the various Yurikuma Arashi adaptations relate to each other?
The "original" author of these anime is a group rather than a single person.

When Kunihiko Ikuhara created Revolutionary Girl Utena, he created the group named Be-Papas and discussed the main story with the group.
The other group members are Chiho Saito who is a manga writer and Youji Enokido who is a story writer.
Ikuhara created the anime version of Utena, and at the same time Saito wrote the manga version of Utena.
They discussed the main story of Utena, but they created the different works independently and the details of each story were different.

Both anime and manga were original works; neither is an adaptation of something.

Ikuhara did same thing for Mawaru Penguindrum and Yuri Kuma Arashi.
The group members are different, but they created main story as a group
and created the manga and anime versions separately.

By creating as a group, they can create a better story. They can also release anime, manga and novel versions at same time; this will lead to better sales by a synergy effect.

Ikuhara is not only person who use group system.
An old robot anime Patlabor was created by the group Head Gear.
For newer example, Madoka Magica was created by the group Magica Quartet.