How is a relationship different from a very intimate friendship, apart from the physical aspects?I have platonic friends with whom I have very emotionally intimate friendships.
I've had friends with benefits with people that I wasn't that emotionally intimate with, as well.
I think you are asking, "do we have a romantic relationship?" and if so, my answer is no, I don't think that you do.
I don't use the word "Relationship" in the way you describe. I have a relationship with the universe, with the postal carrier, with my children, with my mother, with ex-partners...it's just a term that means "set of interactions around a particular set of actors". You have an intense friendship with her, but there are significant gaps in your interaction around honesty and physical intimacy.
So, my own definition of a romantic relationship includes emotional intimacy and the desire for physical intimacy. A communication style founded on mutually agreeable love languages. Some degree of life-entanglement.