The main differences I've gathered so far is that this culture divides people by gender, and has opinions about which genders can be together. The Radchaai find beliefs about gender to be, well, primitive.
We did have marriages, and clientage. The lines between the two are blurred, but clientage can sometimes involve relationships that are neither romantic nor sexual, only formed based on political, social, or financial advantages, whereas marriage can involve any and all of those things but almost always indicates a romantic or sexual aspect.
Outside of those relationships, people generally take lovers as they wish.