Non-cognitivists, in contrast, think that moral discourse is not truth-apt.

Technically, that's not quite right (except for the early emotivists, etc.). Contemporary expressivists and quasi-realists insist that they can capture the truth-aptness of moral discourse (given the minimalist's understanding that to assert 'P is true' is equivalent to asserting just 'P'). So they will generally explain what's distinctive about their metaethics in some other way, e.g. by appeal to the idea that it's our moral attitudes rather than their contents that have a certain central explanatory role...