NoIdeaWhatToDo, the world revolves around semantics, so that's not really an argument. From the rather many posts in this thread, it seems it is at least somewhat important. Maybe not. The female analogy is interesting.

Keegan, I think manic-depression or manic-depressive is quite a valid term still, but it only describes BP-I. I prefer manic-depressive to bipolar disorder I, since few people would have any idea what it stands for.

RxQueen, it is interesting you'd say that: anxiety definitely plays an essential part in the onset and maintenance/persistence (or worsening) of the disorder. More essential still, I find, is the way we respond to anxiety (and stress and excitement).

Whether you use it that way or not, it is remarkable that people use "I am bipolar" while they wouldn't say "I am panic/anxiety" or "I am unipolar anxious" or something. It has probably a lot to do with control, persistence and/or pervasiveness, I guess. But maybe also with the way we look at the world. Somewhat, sometimes very much, more transcending. Not seeing the trees for the forest sometimes, thereby seeing things as more influential or essential to us than they really are, maybe.

Just thinking out loud here: just ignore that.

I use "I have a mood disorder", "I have a psychotic disorder", "I have a bipolar disorder" or "I am a manic-depressive", depending on circumstances/needs-to-know.

I also use, half-jokingly, "I am (a bit) crazy (sometimes)", "I am (a bit) insane (sometimes)", "mood flippin' psychotic", "I am sometimes insanely great, sometimes insanely small.", or something else I think of.

I don't keep it ever a secret really, but I might get cryptic enough or euphemistic enough to get the understanding/acceptance but not the stigma (much of that is also the way you put it: categorical terms usually work counterproductive). Since being cryptic is second nature to me, I really enjoy that, as well: finding the right balance to not be put down as anything in particular but that people still tentatively get it.

Edit:
Wow, that was longer than expected! Sorry about that.

Another edit:
It could also be that not being bipolar also has distinct qualities to it: not just being an absence-of.

Much like the female/male dichotomy.