Well the problem with the distinction is that you're using the word "asexual" to describe three unique situations (well, at least three, anyway).
-Some people make a conscious decision to forgo "rumptie-too" as "I Can Help You" hilariously referred to it. The desire may be there, but either due to social constraints, other focuses in life, or just general ugliness (hey, it happens) they have made the decision not to attempt to have a sexual aspect of their day-to-day business.
-Some people just genuinely have no desire. I don't really care about race cars. Some people love them, and I'm fine with that, but they've no bearing on my life whatsoever. The social (and let's face it biological) norm is generally to involve/entangle yourself with someone. To KNOW them, Biblically and all that, but some people just don't dig that vibe.
-And the third group that comes to mind are people who have the emotional desire, but something is perhaps medically wrong with them so that their bodies do not react as they are biologically supposed to when they should be interested in someone. You ever notice how everyone you have ever been attracted to SMELLS incredible? That's not a coincidence, but some people have this reaction somehow chemically blocked, and they may need the help of a medical professional to solve the problem.
Society has an unwritten list of rules that everyone seems to have an UNDERSTANDING of, and to live your life outside those guidelines is abnormal, but that's such a strange idea to me. I have dated three women in my life, and each one was staggeringly different from the other two, not just in terms of personalities (although they were that. Keep trying til I find the right one, right? Blargh), but also in the details. What they were interested (or not interested) in doing when it was naked time ran a remarkable gamut, and I am not surprised or put off at all to learn that there are people who just have NO interest.
I feel very bad for people in the third category, though. I could never be asexual myself... I just... well I just love women too goddamned much. MAN they're awesome.