In
the anime Chaos was the evil force responsible for all the "bad"
things which happen in the universe. Galaxia went against this force and
sealed it inside her body in an attempt to create peace throughout the galaxy.
Chaos was too strong and eventually started taking over Galaxia's mind and
body. Galaxia was forced to send out her "light of hope" before
she became completely corrupted. Galaxia had made a grave mistake by trying
to take on Chaos herself and only in the end did she realize it. Towards
the end he ( or she ) completely takes over and Galaxia's outfit turns all
black. Usagi is able to free Galaxia from Chaos and seal the force inside
the hearts of everyone so that together they would have the strength to
keep peace.

The Chaos of the manga is slightly the same in the sense that he/she is the evil of the galaxy and responsible for all the pain and suffering which has gone on. Chaos was a star like all others but never was fully formed and stayed inside the Galaxy Cauldron, and in a sense "possessed" the Cauldron. He/she never possessed Galaxia but did corrupt her to the dark side. Chaos wanted control as Galaxia did, but in more of a "chaotic" sense where there was nothing but darkness. Chaos thought that it could overwhelm Sailormoon but in the end all the Sailor Crystals gathered together to break the force apart. Sailor Cosmos later says that in the future Chaos is reborn as Sailor Chaos and becomes all powerful killing almost everyone. While inside the Cauldron, Usagi asks Guardian Cosmos whether Chaos had been destroyed or not. The Guardian responds saying that Chaos is too small to be found and that it was possible for her to be reborn once more... and that is the last we hear about it.

Chaos also appears in the Sera Myu. The first couple times Chaos is played by a guy, then in the later ones it appears they are going by the anime where Galaxia becomes completely possessed and her outfit changes to black. They start to call her Sailor Chaos at this point.