On the other hand, if someone cares only about pain and pleasure — both theirs and other peoples' — and would prefer that everyone's pleasure be maximized and everyone's pain be minimized; but this person is not a moral realist, and has no opinion on what constitutes The Good or thinks there's no fact of the matter about whether an act is right or wrong; well, then this person is not a utilitarian at all. Again, describing this person as a hedonistic or any other kind of utilitarian completely fails to match up with how the term is used in the philosophical literature.

You may be right to say that my use of "utilitarian" is different from how it's conventionally used in the literature

... though, I just looked at the SEP entry on Consequentialism, and I note that aside for the title of one book in the bibliography, nowhere in the article is the word "realism" even mentioned. Nor does there seem to be an entry in the list of claims making up classic utilitarianism that would seem to require moral realism. I guess you could kind of interpret one of these three conditions as requiring moral realism:

Universal Consequentialism = moral rightness depends on the consequences for all people or sentient beings (as opposed to only the individual agent, members of the individual's society, present people, or any other limited group).

Equal Consideration = in determining moral rightness, benefits to one person matter just as much as similar benefits to any other person (= all who count count equally).

Agent-neutrality = whether some consequences are better than others does not depend on whether the consequences are evaluated from the perspective of the agent (as opposed to an observer).

... but it doesn't seem obvious to me why someone who was both an ethical subjectivist couldn't say that "I'm a classical utiliarian, in that (among other things) the best description of my ethical system is that I think that the goodness of an action should be determined based on how it affects all sentient beings, that benefits to one person matter just as much as similar benefits to others, and that the perspective of the people evaluating the consequences doesn't matter. Though of course others could have ethical systems that were not well described by these items, and that wouldn't make them wrong".

Or maybe the important part in your comment was the part "...but this person is not a moral realist, and has no opinion on what constitutes The Good"? But a subjectivist doesn't say that he has no opinion on what constitutes The Good: he definitely has an opinion, and there may clearly be a right and wrong answer with regard to the kind of actions that are implied by his personal moral system; it's just that the thing that constitutes The Good will be different for people with different moral systems.