Moral anti-realists deny that moral values are mind-independent. We have already encountered one version of anti-realism: non-cognitivism, which claims that moral statements are not the sort of things that can be true or false, rather, they are ejaculations roughly equivalent to "Boo!" or "Yuck!"
The flip side of this is moral error theory, associated with J. L. Mackie. Error theory is a cognitivist theory - moral statement are capable of being true or false - but the error theorist claims that, in fact, no such statements are true, because they all reference things (moral values) that don't actually exist.
The moral error theorist stands to morality as the atheist stands to religion. (SEP)
Finally, there is ethical subjectivism, that holds that moral facts exist but are mind-dependent in some way: morality is about mental attitudes rather than about objective moral entities that exist "out there." One version of subjectivism is moral relativism: moral truths are relative to the individual, or to the group to which the individual belongs. However, it is possible to be subjectivist without being relativist, and vice versa.
This completes the overview of the main approaches to ethics. I can't resist adding some comments of my own here.
There seems to be - in the sources I have looked at, at least - considerable tension between prescriptive approaches to ethics (how should one go about making moral decisions) and descriptive ones (how do people actually go about making moral decisions). Some ethical theories (utilitarianism, for example) are clearly intended prescriptively, while others (error theory) just as clearly are not. All these are lumped together under the label "metaethics." It seems to me that these ought to be two completely different disciplines.
On the descriptive side, I have been reading Moral Minds, by Harvard's Marc Hauser. His approach (and that of the researchers he cites) promises to be a game-changer in descriptive ethics. He describes numerous experiments in which people are presented with moral questions (e.g. the famous trolley problems) and must decide what actions are permissible, obligatory, or forbidden. He relates cases of people with various mental impairments and discusses how these illuminate models of moral decision-making. He argues for a Chomskian approach. We are born with some innate ability to learn language, but the specifics of the language we learn are shaped by the linguistic environment in which we grow up. So with morality: we are born with some innate moral capacities, but the specific morality we end up with is shaped by the cultural environment. Whether or not his view turns out to be fruitful, it seems certain that we will learn more about how moral decisions are actually made by way of experiments of this sort than by the armchair speculations of philosophers.
But where does this leave us as far as the prescriptive side of the issue? Does learning about how people make moral judgments help us decide how people ought to make moral judgments? It seems we have here a meta-version of Hume's is-ought problem: no amount of research on how moral judgments are made will tell us how they ought to be made.