Moral realists are those who think that [...] moral claims do purport to report facts and are true if they get the facts right. Moreover, they hold, at least some moral claims actually are true. [...]
As a result, those who reject moral realism are usefully divided into (i) those who think moral claims do not purport to report facts in light of which they are true or false (noncognitivists) and (ii) those who think that moral claims do carry this purport but deny that any moral claims are actually true (error theorists).
Traditionally, to hold a realist position with respect to X is to hold that X exists in a mind-independent manner (in the relevant sense of “mind-independence”). On this view, moral anti-realism is the denial of the thesis that moral properties—or facts, objects, relations, events, etc. (whatever categories one is willing to countenance)—exist mind-independently. This could involve either (1) the denial that moral properties exist at all, or (2) the acceptance that they do exist but that existence is (in the relevant sense) mind-dependent. Barring various complications to be discussed below, there are broadly two ways of endorsing (1): moral noncognitivism and moral error theory. Proponents of (2) may be variously thought of as moral non-ojectivists, or idealists, or constructivists.
So, everyone defines “non-realism” so as to include error theory and non-cognitivism; some people define it so as to also include all or most views on which moral properties are in some sense “subjective.”
These ambiguities seem like good reasons to just avoid the term “realism” and talk about more specific positions, though I guess it works to think about a sliding scale where substantive realism is at one extreme, error theory and non-cognitivism are at the other extreme, and remaining views are somewhere in the middle.
Sayre-McCord in SEP’s “Moral Realism” article:
Joyce in SEP’s “Moral Anti-Realism” article:
So, everyone defines “non-realism” so as to include error theory and non-cognitivism; some people define it so as to also include all or most views on which moral properties are in some sense “subjective.”
These ambiguities seem like good reasons to just avoid the term “realism” and talk about more specific positions, though I guess it works to think about a sliding scale where substantive realism is at one extreme, error theory and non-cognitivism are at the other extreme, and remaining views are somewhere in the middle.