I'm not really sure that's a useful way of putting it. There are a set of observations which don't match expectations, one idea which explains most of them is that there is some matter present that we can't directly observe (and then there's a wide variety of more specific ideas of what the nature of this matter may be, some of which fit observations better than others). That's in contrast to the idea that our theory of gravity may be incorrect, which also explains some of the observations (including ones which dark matter does not), but less of them overall, and there's a wide variety of specific ideas of how we might modify gravity to fit the observations (and generally I think the difficulty is you can come up with modifications that explain one obversation well but it's hard to explain a lot of them at once).
DM and MOND are referring to different ideas of matching the anomolous observations, not the observations themselves. And each is really a family of different theories, as opposed to one singular theory each.