How could one determine which they are? It all seems very nebulous.

I agree! How one could even go about determining if this hypothetical two-type typology has any basis or even is meaningful, I have no good ideas. What I do know is that I've heard lots of bisexual people place themselves into either of the two types. The I'm-bisexual-because-I-like-vulvas-and-penises, or the I'm-bisexual-because-I-care-not. So, I've collected the anecdotes and there's my hypothesis.

Per your bolded question:

That's my question. Is this purely conceptual, or is it a meaningful difference such that there are indeed different sorts of bisexual people. Which, if true, could mean that bisexuality, or plurisexuality (the technical term for the opposite of monosexuality) is fundamentally different. Where bisexuality isn't a continuum from heterosexual to homosexual but could, in some cases, better be understood as its own stand-alone thing, even though you could quantify it.

To rope it into the larger topic, so it's not just me being overly academic, this could explain different bisexual attitudes towards trans people.