I agree with Fuchka; this seems like largely a semantic distinction.
As I read it, you don't like thinking of "the relationship" because to you it implies a duty or a mandated outcome, and for me it doesn't automatically have that association.
If I have a friend or love whose presence in my life I value and want to maintain, but I am having difficulty understanding or communicating with this person, I will put effort into into improving the situation. To me, that would be working (obligation free, out of choice) on our relationship. Maybe you'd rephrase it as each person working on him/herself at the same time together, or working on communication rather than on the relationship, but to me it's not that important of a distinction.
Anyway, thanks for explaining how you see it. I like a bunch of what you write, but this point, which seems particularly important to you, had been puzzling me.