A relationship is a relationship, sex is something that the people in the relationship decide on how to handle. If you all feel you are in a relationship and that the title applies, then it does.
I have told everyone about my situation with Violet and Anne, but haven't mentioned Lana. Our situation with her is very much like you mention with Katja - we took her in from a bad situation, and things progressed - to a point. Lana is straight and Violet is madly in love with her which makes for a lot of sitcom humor in the house; Lana and I were supposed to hook up but it never happened, we became fast freinds though. Lana is very protective of Violet and my relationship, and Anne had to pass the Lana test (she passed with flying colors) before we were allowed to date her seriously, lol. We call her "our girlfreind without benifits", LOL.