I understand one hypothesis is that it is some sort of matter, but the anomaly is that we can't fully account for why galaxies don't fly apart, given our current models and observables. One explanation for the anomaly is that there is stuff which interacts with observable matter in a matter-like way. That is, we don't know there is any new form of matter, rather, one of the conjectures is that the inconsistency we have observed can be explained by positing a new form of matter which interacts with known matter in a way we have not yet experienced or accounted for in previous models.
The point is, the real discovery is not the existence of any new form of matter, because we have not discovered a new form of matter, rather, the discovery is that we've found a very interesting point at which our theories are inconsistent with reality.
That's all more or less true. But what part of dark matter, the name of the conjecture, as you say, or the leading hypothesis, as I say, runs against this description? It does not imply that it's the only hypothesis, it does not imply that we discovered dark matter. Btw, stuff which interacts matter-like /is/ matter.
I've had a number of discussions with lay-folk who think we have in fact discovered a new/exotic form of matter. That is what gets lost. What we have discovered is that something went wrong in our predictions, which could be explained as a new form of matter (or more than one new form of matter), but, could also be explained by changing our models in any number of ways, etc. This is not at all obvious to the public.
I say "we" in the broadest sense of physicists, as I did study that for my grad/undergrad, but do not practice in the field (I now do the computering).
That may well be the case, but that is not caused by the term "dark matter", but by people not making enough of an effort to distinguish between leading hypothesis and discovery. That could happen with pretty much any name.
I'm pretty sure it wouldn't happen with the term Dark Hypothesis, or Dark Inconsistency. Or something cooler than those :^) . I think the words 'matter' and 'energy' are the confusion because they are already overloaded with meaning, even if not properly understood by the public, they still have some sort of idea of what those are.
It might be interesting if we had a standard, and publicly known, word or phrase used when talking about scientific results that find an inconsistency between reality and theory (not just slang). Like, "today physicists discovered a Theory Bug when applying Einstein's general relativity to galaxies" or some such. Something cooler than that though.
The point is, the real discovery is not the existence of any new form of matter, because we have not discovered a new form of matter, rather, the discovery is that we've found a very interesting point at which our theories are inconsistent with reality.