Again, it is possible to fail in many ways, while to succeed is possible only in one way. – Aristotle.
According to moral realists, like me, the sentence, “Murder is wrong,” means that murder, in fact, is wrong. Such sentences are capable of being either true or false; this one happens to be true. It describes the actual moral quality of murder, a property which belongs to the act irrespective of what any of us think, feel, or say about the matter. If I say “Murder is right,” murder is still wrong.
In everyday speech we tend to use the term “relativism” as a catch-all for a variety of views which are actually somewhat different. What they have in common is that they reject moral realism. But they go off the rails for different reasons.
The three most common kinds of moral anti-realism are relativism in the strict sense of the term, subjectivism, and non-cognitivism. To the relativist in the strict sense, the sentence “Murder is wrong” means that murder is wrong in relation to the speaker. Such sentences may be true for one person or group, he thinks, but false for another. Maybe murder isn’t wrong for, say, assassins.
To the subjectivist, the sentence “Murder is wrong” may seem to tell us something about murder, but in fact it only tells us something about the speaker. One well known variety of subjectivism holds that what it tells us about the speaker is his feelings about murder – perhaps something like, “I dislike it, and I want you to dislike it too.” If the subjectivist says that such sentences are capable of being true or false – and he may not -- at best he means that they might be either correct or incorrect descriptions of the speaker’s emotions. “It’s all about you.”
To the non-cognitivist, although the utterance “Murder is wrong” has the grammatical form of a sentence, it does not actually express a proposition at all. Consequently it is no more capable of being true or false than an utterance like “Whoops,” “blimey,” or “I’ll be dog-goned.”