I'm not sure this taxonomy is helpful from David Pearce's perspective. David Pearce's position is that there are universally motivating facts - facts whose truth, once known, is compelling for every possible sort of mind. This reifies his observation that the desire for happiness feels really, actually compelling to him and this compellingness seems innate to qualia, so anyone who truly knew the facts about the quale would also know that compelling sense and act accordingly. This may not correspond exactly to what SEP says under moral realism and let me know if there's a standard term, but realism seems to describe the Pearcean (or Eliezer circa 1996) feeling about the subject - that happiness is really intrinsically preferable, that this is truth and not opinion.

From my perspective this is a confusion which I claim to fully and exactly understand, which licenses my definite rejection of the hypothesis. (The dawning of this understanding did in fact cause my definite rejection of the hypothesis in 2003.) The inherent-desirableness of happiness is your mind reifying the internal data describing its motivation to do something, so if you try to use your empathy to imagine another mind fully understanding this mysterious opaque data (quale) whose content is actually your internal code for "compelled to do that", you imagine the mind being compelled to do that. You'll be agnostic about whether or not this seems supernatural because you don't actually know where the mysterious compellingness comes from. From my perspective, this is "supernatural" because your story inherently revolves around mental facts you're not allowed to reduce to nonmental facts - any reduction to nonmental facts will let us construct a mind that doesn't care once the qualia aren't mysteriously irreducibly compelling anymore. But this is a judgment I pass from reductionist knowledge - from a Pearcean perspective, there's just a mysteriously compelling quality about happiness, and to know this quale seems identical with being compelled by it; that's all your story. Well, that plus the fact that anyone who says that some minds might not be compelled by happiness, seems to be asserting that happiness is objectively unimportant or that its rightness is a matter of mere opinion, which is obviously intuitively false. (As a moral cognitivist, of course, I agree that happiness is objectively important, I just know that "important" is a judgment about a certain logical truth that other minds do not find compelling. Since in fact nothing can be intrinsically compelling to all minds, I have decided not to be an error theorist as I would have to be if I took this impossible quality of intrinsic compellingness to be an unavoidable requirement of things being good, right, valuable, or important in the intuitive emotional sense. My old intuitive confusion about qualia doesn't seem worth respecting so much that I must now be indifferent between a universe of happiness vs. a universe of paperclips. The former is still better, it's just that now I know what "better" means.)

But if the very definitions of the debate are not automatically to judge in my favor, then we should have a term for what Pearce believes that reflects what Pearce thinks to be the case. "Moral realism" seems like a good term for "the existence of facts the knowledge of which is intrinsically and universally compelling, such as happiness and subjective desire". It may not describe what a moral cognitivist thinks is really going on, but "realism" seems to describe the feeling as it would occur to Pearce or Eliezer-1996. If not this term, then what? "Moral non-naturalism" is what a moral cognitivist says to deconstruct your theory - the self-evident intrinsic compellingness of happiness quales doesn't feel like asserting "non-naturalism" to David Pearce, although you could have a non-natural theory about how this mysterious observation was generated.