what's in a relation?

I was preparing for my theory course this afternoon and got completely hung up on the difference between the words "relation" and "relationship." What IS the difference? What does it mean when I say "the relationship between A and B" and "the relation between A and B"? Can A and B even have a relation?

These are questions worth a good afternoon's stymying. Almost as good as the time when I spent an afternoon researching whether dogs have belly buttons (they do, but they look a little different from ours.....it's a long story).

So, being a sensible person and not wanting to abuse the English language any more than absolutely necessary (through my usual uncontrollable stuttering and/or slamming together of metaphors), I looked the two words up in my Websters New Collegiate Dictionary. And here is what I found:

a relation is a quality.
a relationship is a state or character.

Now that's helpful (NOT)! Only, what do they mean when they distinguish between a quality and a state? By state do they mean state of being? As in, "quietude" is a state and "blueness" is a quality? But can't "blueness" be a state, too?

I was still baffled. So then I did my trusty Google search, which remains my favorite way of finding out important information (that's how I found out about the dogs and the belly buttons, after all).

And so my internet search led me to this nifty page, where I discovered that a relation is "a set of attributes in a relation that exactly matches a primary key in another relation," whereas a relationship is identified as "man:one," or "a relationship between A and B."

Notwithstanding the major no-no of using the term in question to define itself, I find this more spelled-out example extremely unilluminating. I still just don't get it. There seems to be a quantifiable difference between relations and relationships--everyone says so!--but I can't seem to put my finger on the rule.

Do "relations" connote structural interdependencies, while "relationships" refer to the actual state of being in an interdependency? This is the closest I can come to a good operating definition, yet when I think about the difference between those two statements I am hard put to explain why they are different.

And so I leave it at that. If someone has a better way of explaining things, will they please let me know?