Ceoli's post # 2 was quite refreshing, and goes a long way toward letting us all off the hook. That is, it helps us to recognize that all of our relationships are both unique and ... well, just as they are. We don't have to force standard categories upon them.
Since this IS the topic of non-sexual intimacy, I'd also like to bring up the flip side of this, since I seem to be in the midst of this right now, and it's really delicate for me.
I don't like to "define" my relationships. I sincerely believe that EVERY relationship should be taken for what it is, without closing any doors. Doing so just stunts everything. I don't think there's a single aspect of any relationships that can't be addressed while respecting the will and values of the people in it. Perhaps two people might disagree on where that relationship is heading, but even that can be addressed.
But not everybody is poly. Even those that are set the boundaries of themselves to be different in every relationship. I have had issues with partners of my friends NOT being comfortable with the fact that I'm open with my relationships and feel jealous that I refuse to define them. Intellectually, I know that this is something in THEIR relationship that needs to be worked out, but it's not something I can avoid. People who are mono feel possessive sometimes, and they sometimes demand this sort of classification. As a result, I find that I do "define" my relationships though perhaps it's more complicated than using simple terminology, with all kinds of twists and turns. I love my friends with great, big portions of my heart, but saying this to a boyfriend who considers you a rival doesn't always convey the same sort of affection that I mean.
Granted, I'm also an iconoclast. I'm a political activist, and I like cutting right through bullshit. This isn't a poly thing per se, but my stance on relationships and defintions clashes with who I am, and while I don't consider it either unhealty OR damaging to myself or others, it DOES affect things and my relationship with folks, and potentially the relationships of people I care deeply about.
There's also the other side. Another friend of mine rigidly defines themselves. This friend also seems to have some sort of issues with intimacy and sexuality where they're defensive and guarded towards people they are sexually interested in (or defines that they might be) but can be extremely open, honest and intimate with people they ignore sexually.
I'm also extremely attracted to this last person, and to say that the defintion of the relationship doesn't affect me would be silly and dishonest. But since I love then and value them, I don't want to make them uncomfortable by crossing that boundary of sexual interest.
And I think that's what the "definition" and "categorization" of relationships are, ultimately. The understanding and honoring of boundaries.