So I made a post about some of this before so I'll try not to repeat unnecessary details.
I have a Master. We are monogamous, exclusive. BUT I also have a slave/pup (online) that I don't do anything sexual with and my Master is okay with it. My slave, N, shows me his chastity cage so I do see him naked but I don't send him anything sexual at all. He can see my blog with my nudes but he never gets sexual photos from me personally. And he's okay with this. N obeys my every command and I tell him what to do all the time but that's it. He also became a pup because of me.
Master has never directly communicated with N and he's not really interested in doing so, but he still get's the final say on things. So if there's something he doesn't want me to do, I can't do it. For example, even if I wanted to send nudes to N, Master says I'm not allowed. N also obeys my Master. I'm okay with this of course.
So what would one call this relationship? I'm not emotionally attached to this slave, ESPECIALLY not the same way I am with Master, but N loves me with all his heart and lives to serve me. I do care about him, as he is my slave, but it does not exceed friendship-level caring for me. But everyone involved is happy this way and I never intend to cheat on my Master and everything I do with N is with his permission.